A campus survey of OWLs indicates that 7% are charming, 4% are modest, and 3% are both charming and modest. Find the probability that an OWL is modest, given that he/she is charming. Given that a student isn't modest, what is the probability that they are not charming?

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carlosego carlosego · Answer 1 · 2019-02-03T21:09:13+01:00

Answer:

P(modest | charming) = 0.4286

P(not charming | not modest) = 0.896

Step-by-step explanation:

This is a conditional probability problem.

Let A and B be two dependent events, then:

The probability of A given B is written as:

P (A | B) = [tex]\frac{P(A\ and\ B)}{P(B)}[/tex]

So:

The probability that an OWL is modest given that he/she is charming is:

P (modest | charming) = [tex]\frac{P(modest\ and\ charming)} {P(charming)}[/tex]

P (modest | charming) = [tex]\frac{0.03}{0.07}[/tex]

P (modest | charming) = 0.4286

Then, the probability that a student is not modest is:

[tex]1- P(modest) = 1 - 0.04 = 0.96[/tex]

The probability that a student is not charming and not modest is:

[tex]1- [P(charming\ or\ modest)]\\\\ = 1-[0.07 + 0.04 - 0.03]= 0.92[/tex]

So:

P(not charming | not modest) = [tex]\frac{P(not\ charming\ and\ not\ modest)}{P(not\ modest)}[/tex]

P(not charming | not modest) =[tex]\frac{0.92}{0.96}[/tex]

P(not charming | not modest) = 0.9583