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 [tex]P(B|G) = \frac{2}{3}[/tex]
Step-by-step explanation:
The sample size is [tex]n = 80[/tex]
The friend of the groom are [tex]G = 30[/tex]
The friend of the groom are [tex]B = 29[/tex]
The friend of both bride and groom are [tex]Z = 20[/tex]
The probability that a guest is a friend of the bride is mathematically represented as
[tex]P(B) = \frac{29}{80}[/tex]
The probability that a guest is a friend of the groom is mathematically represented as
[tex]P(G) = \frac{30}{80}[/tex]
The probability that a guest is both a friend of the bride and a friend of the groom is mathematically represented as
[tex]P(B \ n \ G) = \frac{20}{80}[/tex]
Now
[tex]P(B|G)[/tex] is mathematically represented as
[tex]P(B|G) = \frac{P(B \ n \ G)}{P(G)}[/tex]
Substituting values
[tex]P(B|G) = \frac{\frac{20}{80} }{\frac{30}{80} }[/tex]
[tex]P(B|G) = \frac{2}{3}[/tex]
Answer:
the answer is 3/5
Step-by-step explanation:
on Khan
