Question

a coin is flipped and a number cube is rolled. the tree - diagram below shows the possible outcomes. use the diagram to answer the questions. coin number cube outcome 1 (heads, 1) 2 (heads, 2) 3 (heads, 3) heads 4 (heads, 4) 5 (heads, 5) 6 (heads, 6) 1 (tails, 1) 2 (tails, 2) 3 (tails, 3) tails 4 (tails, 4) 5 (tails, 5) 6 (tails, 6) (a) how many outcomes are there? outcome(s) (b) how many outcomes involve rolling a 5 or a 6? outcome(s) (c) how many outcomes involve heads and an even number? outcome(s)

Explanation:

Step1: Calculate total outcomes

The coin - flip has 2 outcomes (heads or tails) and the number - cube roll has 6 outcomes. By the fundamental counting principle, the total number of outcomes is the product of the number of outcomes of each event. So, \(2\times6 = 12\).

Step2: Count outcomes with 5 or 6 on cube

For each of the 2 coin - flip outcomes (heads and tails), there are 2 outcomes of the number - cube roll that are 5 or 6. So, \(2\times2=4\).

Step3: Count outcomes with heads and even number

The even numbers on the number - cube are 2, 4, 6. When the coin shows heads, there are 3 such outcomes. So the number of outcomes is 3.

Answer:

(a) 12
(b) 4
(c) 3