The usher at a wedding asked each of the 80 guests whether they were a friend of the bride or of the groom. Here are the results: In this sample, are the events "bride" and "groom" mutually exclusive?

Complete Question

Calculating conditional probability

The usher at a wedding asked each of the 80 guests whether they were a friend of the bride or of the groom.

Here are the results:

Bride :29

Groom :30

BOTH : 20

Given that a randomly selected guest is a friend of the groom, find the probability they are a friend of the bride.

P (bride | groom)​

The probability is

Step-by-step explanation:

The sample size is

The friend of the groom are

 The friend of the groom are

 The friend of both bride and groom are

The probability that a guest is a friend of the bride is mathematically represented as

The probability that a guest is a friend of the groom is mathematically represented as

The probability that a guest is both a friend of the bride and a friend of the groom is mathematically represented as

Now

    is mathematically represented as

     Substituting values