Question

list all the elements of the sample space for the following experiment. you spin a spinner with four equal - sections labeled 1, 2, 3, and 4 and toss a dime. a. (1, h), (2, h), (3, h), (4, h), (1, h), (2, h), (3, h), (4, h) b. (1, h), (2, h), (3, h), (4, h), (1, t), (2, h), (3, h), (4, h) c. (1, t), (2, t), (3, t), (4, t), (1, t), (2, t), (3, t), (4, t) d. (1, h), (h, 1), (2, h), (h, 2), (3, h), (h, 3), (4, h), (h, 4), (1, t), (2, t), (3, t), (4, t) please select the best answer from the choices provided. o a o b o c o d

Explanation:

Step1: Analyze the two - part experiment

The spinner has 4 sections labeled 1, 2, 3, 4 and the coin has 2 outcomes (H - heads and T - tails).

Step2: Use the counting principle

The total number of elements in the sample space is the product of the number of outcomes of the spinner and the number of outcomes of the coin toss. There are 4 outcomes for the spinner and 2 for the coin, so there are \(4\times2 = 8\) elements in the sample space. The elements are pairs where the first element is from the spinner (1, 2, 3, 4) and the second is from the coin (H or T). The sample - space is \(\{(1,H),(1,T),(2,H),(2,T),(3,H),(3,T),(4,H),(4,T)\}\).

Answer:

C. \((1, T),(2, T),(3, T),(4, T),(1, H),(2, H),(3, H),(4, H)\)