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Giving a test to a group of students, the grades and gender are summarized below A...

Giving a test to a group of students, the grades and gender are summarized below

A B C Total
Male 6 11 2 19
Female 10 13 15 38
Total 16 24 17 57



If one student is chosen at random,

Find the probability that the student was NOT a female that got a "B"

Solutions

Expert Solution

We have to find the probability that the selected student was Not a female given that got a B

Using the formula P(A|B) = P(not a female AND got a B)/P(got a B)

we can write P(Not a female given that got a B) = P(not a female AND got a B)/P(got a B).......equation 1

First, we will find the probability that the selected student is not a female AND got a B

total students = 57 and not a female means male only = 11

we have favourable outcome= 11 and total outcome = 57

So, P(not a female AND got a B) = 11/57

Now, probability of getting a B = favourable/total

favourable outcome for getting a B = 24 and total outcome = 57

So, P( got a B) = 24/57

setting the value of P(not a female AND got a B) and P( got a B) in the formula in equation 1

we get

P(Not a female given that got a B) = P(not a female AND got a B)/P(got a B) = (11/57)/(24/57) = 11/24 or 0.4583

Therefore, required probability is 11/24 or 0.4583

milcah answered 1 year ago
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