Question

Calculating conditional probability

G
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
Groom
29
30
20
1
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 1

the answer is 3/5

Explanation:

on Khan

Answer 2

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) = (2)/(3)`

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) = (29)/(80)`

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

`P(G) = (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) = (20)/(80)`

Now

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

`P(B|G) = (P(B \ n \ G))/(P(G))`

Substituting values

`P(B|G) = ((20)/(80) )/((30)/(80) )`

`P(B|G) = (2)/(3)`