I need help with this question please i would appreciate the answer a lot

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julie47d

07.04.2021

Mathematics

$\dfrac{33}{79}$

Step-by-step explanation:

Let F= Applicants are Females.

G= Applicants have a graduate degree.

Given : Total applicants N= 350

Total applicants are females n(F)= 158

Number of applicants are females and have a graduate degree. n(F∩G)=66

Now, Probability that an applicant is female = $P(F)=\dfrac{n(F)}{N}=\dfrac{158}{350}$

Probability that an applicant is female and have a graduate degree:

$P(F\cap G)=\dfrac{n(F\cap G)}{N}\\\\=\dfrac{66}{350}$

Then, the probability that a randomly chosen applicant has a graduate degree, given that they are female :-

$P(G|F)=\dfrac{P(F\cap G)}{P(F)}$ [By conditional probability formula.]

$P(G|F)=\dfrac{\dfrac{66}{350}}{\dfrac{158}{350}}\\\\=\dfrac{66}{158}\\\\=\dfrac{33}{79}$

Hence, the required answer = $\dfrac{33}{79}$

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