Question

Probability question! Hoping to get a full explanation for this so I can learn step by step.

A hair salon surveyed 289 customers (139 females and 150 males) to see if they are satisfied with the service. The result is summarized in the following table.

If we know the selected customer is a female, then what is the probability that she is satisfied?

P(satisfied|female) =

How about the probability that a randomly selected customer is a female if we know that the person is satisfied?

P(female|satisfied) =

	Satisfied	Not Satisfied	Total
Female	112	27	139
Male	137	13	150
Total	249	40	289

Answer 1

Solution(1)
These both questions are Conditional probability condition:
Solution(a):
P(Satisfied | Females) = P(Satisfied and Females)/ P(Females)
From the Given table we found
P(Satisfied | Female) = (112/289)/(139/289) = 112/139 = 0.8057
So there is 80.57% that she is satisfied when we know the selected customer is a female.

Solution(2)

P(Female | Satisfied) = P(Females and Satisfied)/ P(Satisfied)
= (112/289)/(249/289) = 112/249 = 0.4498
So there is 44.98% that customer is female if we know that the person is satisfied.