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Out of 350 applicants for a job, 158 are female, and 66 are female and have a graduate degree.

Step 1: What is the probability that a randomly chosen applicant has a graduate degree, given that they are female?

Answer :

Total applicants = 350

Total female that have a degree = 66

Probability = 66/350 = 33/175

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Answer: The probability of choose a female with a degree is 33/175.
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Rewritten by : Barada

Answer: [tex]\dfrac{33}{79}[/tex]

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 = [tex]P(F)=\dfrac{n(F)}{N}=\dfrac{158}{350}[/tex]

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

[tex]P(F\cap G)=\dfrac{n(F\cap G)}{N}\\\\=\dfrac{66}{350}[/tex]

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

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

[tex]P(G|F)=\dfrac{\dfrac{66}{350}}{\dfrac{158}{350}}\\\\=\dfrac{66}{158}\\\\=\dfrac{33}{79}[/tex]

Hence, the required answer = [tex]\dfrac{33}{79}[/tex]