Question

someone please answer June is conducting an experiment using a quarter, a nickel, and a six-sided number cube. Her experiment consists of tossing both coins and rolling the number cube. create a tree diagram, or list of all of the possible outcomes for her experiment. (please explain this thoroughly)


Part B
What is the probability that the coins don't come up the same (i.e., heads and tails or tails or heads) and the cube shows a prime number? Record your answer as a percent rounded to the nearest tenth.

Answer 1

Part A)
You can get any of the numbers 1 through 6 on the number cube, and either heads (H) or tails (T) on either coin at one time.  This gives us the sample space
{(1, H, H), (1, H, T), (1, T, H), (1, T, T)
(2, H, H), (2, H, T), (2, T, H), (2, T, T)
(3, H, H), (3, H, T), (3, T, H), (3, T, T)
(4, H, H), (4, H, T), (4, T, H), (4, T, T)
(5, H, H), (5, H, T), (5, T, H), (5, T, T)
(6, H, H), (6, H, T), (6, T, H), (6, T, T)}

Part B)  
There are 8 outcomes that fit these criteria (coins come up differently and prime number) out of a total of 24 outcomes, so the probability is 8/24=1/3.