Mathematics: Please help me until I hit 90% I really need to and it’s due at 11:50pm! PLEASE

Please help me until I hit 90% I really need to

dijonmckenzie3

11.04.2020

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

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

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

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

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