SOLUTION: The probability that a student will graduate with honors and get a good job is 0.09 whereas the probability that a student will graduate with honors is 0.1. What is the probability

Question 1017571: The probability that a student will graduate with honors and get a good job is 0.09 whereas the probability that a student will graduate with honors is 0.1. What is the probability that a student will get a good job if she graduates with honors? ans: 90% how ?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let a be the event that she graduates with honors.
let b be the event that she gets a good job.
let (a and b) be the event that she graduates with honors and gets a good job.

p(a) = .1
p(a and b) = .09.

the formula you need to use is:

p(b given a) = p(a and b) / p(b)

this means that the probability that she gets a good job given that she has graduated with honors is equal to the probability that (she has graduated with honors and gets a good job) divided by the probability that (she graduated with honors).

p(b given a) = p(a and b) / p(b) becomes:

p(b given a) = .09 / .1 = .9 = 90%.

logically, this would look like this.

9% of the population graduates with honors and gets a good job.

10% of the population graduates with honors.

given that a person graduated with honors, then then the probability that the person gets a good job is 9% / 10% which is equal to .09/.10 which is equal to 9/10 which is equal to .9 which is equal to 9%.

if 100 persons graduated, then:

9 of them graduated with honors and got a good job.
10 of them graduated with honors.
given that a person graduated with honors, the probability that the person also got a good job is 9/10.

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