Question

Erin uses a spinner divided into four equal sections to decide which drink she’ll have with her lunch. The sections represent water, milk, lemonade, and tea. If she spins the spinner three days in a row, what is the probability that she drinks lemonade one day, tea one day, and water one day? Complete the steps below to find the sample space and solve the problem. PART A - Create a list of all the possible outcomes for three days of drink selections. Use the abbreviations W, M, T, and L to represent water, milk, tea, and lemonade. PART B - Based on the list you created in part A, how many possible outcomes are there? PART C - What is the probability that Erin drinks lemonade one day, tea one day, and water one day? PART D - What is the probability that Erin drinks water two days and lemonade one day?

Answer 1

Part A

W W W M W W T W W L W W

W W M M W M T W M L W M

W W T M W T T W T L W T

W W L M W L T W L L W L

W M W M M W T M W L M W

W M M M M M T M M L M M

W M T M M T T M T L M T

W M L M M L T M L L M L

W T W M T W T T W L T W

W T M M T M T T M L T M

W T T M T T T T T L T T

W T L M T L T T L L T L

W L W M L W T L W L L W

W L M M L M T L M L L M

W L T M L T T L T L L T

W L L M L L T L L L L L

Part B

There are 64 possible outcomes. The sample size is 64.

Part C

To find the probability that Erin drinks lemonade one day, tea one day, and water one day, consider all the cases in which L, T, and W occur one time. Because the order doesn't matter in this scenario, these six outcomes from the list represent the desired event: W T L, T W L, T L W, W L T, L W T, and L T W.

The size of the sample space is 64. So, the probability that Erin drinks lemonade one day, tea one day, and water one day is 3/32.

Part D

To find the probability that Erin drinks water on two days and lemonade one day, we consider all the cases in which two Ws and one L occur. Because the order doesn't matter in this scenario, these three outcomes from the list represent the event: W W L, W L W, and L W W.

The size of the sample space is 64. So, the probability that Erin drinks water two days and lemonade one day is 3/64

Explanation: