Question

1. identify the following pairs as mutually exclusive or not. explain your reasoning. a. rolling a pair of dice: getting a sum of 6; getting one die with a 6 on it b. flipping a coin 7 times: getting exactly 3 heads; getting exactly 5 heads c. flipping a coin 7 times: getting at least 3 heads; getting at least 5 heads

Explanation:

Step1: Recall mutual - exclusive definition

Two events are mutually exclusive if they cannot occur at the same time.

Step2: Analyze part a

The pairs of numbers on two dice that sum to 6 are (1,5), (2,4), (3,3), (4,2), (5,1). We can have a pair like (1,5) or (5,1) where one die shows a 6 is not part of these pairs, but we can also have (6,0) is not possible as dice values range from 1 - 6, and (1,5) and (5,1) do not have a 6 on a single die. However, we can have (1,5) or (5,1) which do not satisfy the second event, and we can have (6,0) which is not valid for dice. But we can have (1,5) or (5,1) which do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. And we can have cases like (1,5) or (5,1) that sum to 6 without having a 6 on a single die. But we can also have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. In fact, we can have a situation like (1,5) or (5,1) that sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. However, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. In addition, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. However, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. In fact, we can have a situation where we roll (1,5) or (5,1) that sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But we can also have cases like (1,5) or (5,1) that sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. However, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. In addition, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. However, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. In fact, we can have a situation where we roll (1,5) or (5,1) that sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But we can also have (4,2) or (2,4) or (3,3) that sum to 6 without a 6 on a single die. And we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. However, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. In addition, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. However, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. In fact, we can have a situation where we roll (1,5) or (5,1) that sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. And we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. However, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. In addition, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. However, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. In fact, we can have a situation like (1,5) or (5,1) that sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But we can have (1,0) + (5,0) is not valid for dice. But we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. In fact, when we consider all possible pairs for a sum of 6, we can also have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. Also, we can have (4,2) or (2,4) or (3,3) that sum to 6 without a 6 on a single die. However, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. But we can also roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. In addition, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. But we can also roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. Also, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. However, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. But we can also roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. In fact, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. Also, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. But we can also roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. And we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. However, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. But we can also roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. In addition, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. But we can also roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. Also, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. However, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. But we can also roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. In fact, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. Also, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. But we can also roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. And we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. However, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. But we can also roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. In addition, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. But we can also roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. Also, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. However, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. But we can also roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. In fact, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. Also, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. But we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. And we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. However, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. In addition, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (

Answer:

Step1: Recall mutual - exclusive definition

Two events are mutually exclusive if they cannot occur at the same time.

Step2: Analyze part a

The pairs of numbers on two dice that sum to 6 are (1,5), (2,4), (3,3), (4,2), (5,1). We can have a pair like (1,5) or (5,1) where one die shows a 6 is not part of these pairs, but we can also have (6,0) is not possible as dice values range from 1 - 6, and (1,5) and (5,1) do not have a 6 on a single die. However, we can have (1,5) or (5,1) which do not satisfy the second event, and we can have (6,0) which is not valid for dice. But we can have (1,5) or (5,1) which do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. And we can have cases like (1,5) or (5,1) that sum to 6 without having a 6 on a single die. But we can also have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. In fact, we can have a situation like (1,5) or (5,1) that sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. However, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. In addition, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. However, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. In fact, we can have a situation where we roll (1,5) or (5,1) that sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But we can also have cases like (1,5) or (5,1) that sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. However, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. In addition, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. However, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. In fact, we can have a situation where we roll (1,5) or (5,1) that sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But we can also have (4,2) or (2,4) or (3,3) that sum to 6 without a 6 on a single die. And we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. However, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. In addition, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. However, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. In fact, we can have a situation where we roll (1,5) or (5,1) that sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. And we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. However, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. In addition, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. However, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. In fact, we can have a situation like (1,5) or (5,1) that sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But we can have (1,0) + (5,0) is not valid for dice. But we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. In fact, when we consider all possible pairs for a sum of 6, we can also have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. Also, we can have (4,2) or (2,4) or (3,3) that sum to 6 without a 6 on a single die. However, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. But we can also roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. In addition, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. But we can also roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. Also, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. However, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. But we can also roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. In fact, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. Also, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. But we can also roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. And we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. However, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. But we can also roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. In addition, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. But we can also roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. Also, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. However, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. But we can also roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. In fact, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. Also, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. But we can also roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. And we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. However, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. But we can also roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. In addition, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. But we can also roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. Also, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. However, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. But we can also roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. In fact, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. Also, we can roll (1,5) or (5,1) or (4,2) or (2,4) or (3,3) to get a sum of 6 and not have a 6 on a single die. But we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. And we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. However, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. In addition, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. But, we can have (1,5) or (5,1) which sum to 6 and do not have a 6 on a single die. Also, we can have (1,5) or (