A study conducted at a certain college shows that 54% of the school's graduates move to a different state after graduating. Find the probability that among 7 randomly selected graduates, at least one moves to a different state after graduating.

99.56% probability that among 7 randomly selected graduates, at least one moves to a different state after graduating.

Step-by-step explanation:

For each graduate, there are only two possible outcomes. Either they move to a different state, or they do not. The probability of a graduate moving to a different state is independent of other graduates. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

54% of the school's graduates move to a different state after graduating.

This means that

7 randomly selected graduates

This means that

Find the probability that among 7 randomly selected graduates, at least one moves to a different state after graduating.

Either none moves, or at least one does. The sum of the probabilities of these events is 1. So

We want . Then

In which

99.56% probability that among 7 randomly selected graduates, at least one moves to a different state after graduating.

a

step-by-step explanation: