Question

Four families randomly select a month for vacation. Find the probabilities.

A. They all pick May.
B. None pick May.
C. They all pick different months.
D. They all pick the same month.

Answer 1

To find the probabilities, we consider the total outcome space and the desired outcomes for each event. The probabilities for each scenario are: A. 1/12, B. 11/12, C. (12*11*10*9)/(12*12*12*12), and D. 12/(12*12*12*12).

Step-by-step explanation:

To find the probabilities for the given scenario, we need to understand the total number of possible outcomes and the specific outcomes required for each event.

A. They all pick May: If all four families pick May, there is only 1 possible outcome out of 12 months, so the probability is 1/12.

B. None pick May: If none of the four families pick May, there are 11 possible outcomes out of 12 months, so the probability is 11/12.

C. They all pick different months: If each family picks a different month, there are 12*11*10*9 possible outcomes out of 12*12*12*12, so the probability is (12*11*10*9)/(12*12*12*12).

D. They all pick the same month: If all four families pick the same month, there are 12 possible outcomes out of 12*12*12*12, so the probability is 12/(12*12*12*12).