Question

Christine Wong has asked Dave and Mike to help her move into a new apartment on Sunday morning. She has asked them both, in case one of them does not show up. From past experience, Christine knows that there is a 47% chance that Dave will not show up and a 37% chance that Mike will not show up. Dave and Mike do not know each other and their decisions can be assumed to be independent. a. What is the probability that both Dave and Mike will show up

Answer 1

0.3339 = 33.39% probability that both Dave and Mike will show up

Explanation:

Probability of independent events:

If A and B are independent events, the probability of both happening at the same time is given by:

`P(A \cap B) = P(A)P(B)`

In this question:

Event A: Dave shows up.

Event B: Mike shows up.

Christine knows that there is a 47% chance that Dave will not show up and a 37% chance that Mike will not show up.

This means that
`P(A) = 1 - 0.47 = 0.53, P(B) = 1 - 0.37 = 0.63`.

a. What is the probability that both Dave and Mike will show up

`P(A \cap B) = P(A)P(B) = 0.53*0.63 = 0.3339`

0.3339 = 33.39% probability that both Dave and Mike will show up