In a survey of adults throughout the caribbean 75% strongly support Caribbean integration. You randomly select 24 adults, throughout the Caribbean, and ask each if they strongly support Caribbean integration.

What is the probability that at most 15 adults say they strongly support Caribbean integration?

To find the probability that at most 15 adults say they strongly support Caribbean integration, we need to calculate the probability of each possible outcome and sum them up.

First, let's find the probability of each specific outcome:

1. 0 adults support integration:
The probability of an adult not supporting integration is 1 - 0.75 = 0.25.
P(0 adults support integration) = (0.25)^24

2. 1 adult supports integration:
The probability of one adult supporting integration is 0.75, and the probability of 23 adults not supporting integration is 0.25.
P(1 adult supports integration) = 24C1 * (0.75)^1 * (0.25)^23

3. 2 adults support integration:
The probability of two adults supporting integration is (0.75)^2, and the probability of 22 adults not supporting integration is (0.25)^22.
P(2 adults support integration) = 24C2 * (0.75)^2 * (0.25)^22

Continue this pattern for 3, 4, 5, ..., 15 adults supporting integration.

Finally, calculate the sum of the probabilities for each specific outcome:

P(at most 15 adults support integration) = P(0 adults support integration) + P(1 adult supports integration) + P(2 adults support integration) + ... + P(15 adults support integration)

Note: P(15 adults support integration) is calculated the same way as the previous outcomes.

Add up all the probabilities, and you will get the probability that at most 15 adults say they strongly support Caribbean integration.