Question

Calculating conditional probability

Answer 1

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)​

Answer:

The probability is $P(B|G) = \frac{2}{3}$

Step-by-step explanation:

The sample size is $n = 80$

The friend of the groom are $G = 30$

 The friend of the groom are $B = 29$

 The friend of both bride and groom are $Z = 20$

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

      $P(B) = \frac{29}{80}$

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

       $P(G) = \frac{30}{80}$

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

       $P(B \ n \ G) = \frac{20}{80}$

Now

    $P(B|G)$ is mathematically represented as

     $P(B|G) = \frac{P(B \ n \ G)}{P(G)}$

     Substituting values

       $P(B|G) = \frac{\frac{20}{80} }{\frac{30}{80} }$

      $P(B|G) = \frac{2}{3}$