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Out of 350350 applicants for a job, 163163 are male and 5656 are male and have a graduate degree. step 2 of 2 : if 9595 of the applicants have graduate degrees, what is the probability that a randomly chosen applicant is male, given that the applicant has a graduate degree? express your answer as a fraction or a decimal rounded to four decimal places.

Respuesta :

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This problem requires the knowledge of conditional probability. Conditional probability is a probability that an event B will occur given event A. We can get this probability through the formula:

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

In the case of the problem, P(A) would be the probability that a randomly chosen applicant has a graduate degree while P(A and B) would be the probability that a randomly chosen applicant is a male AND has a graduate degree. We need to solve for P(B|A) where the chosen applicant is male given that the applicant has a graduate degree.

[tex]P(A)= \frac{95}{350}=0.2714 [/tex]
[tex]P(AandB)= \frac{56}{350}=0.16 [/tex]
[tex]P(B|A)= \frac{0.16}{0.2714}=0.5895 [/tex]

ANSWER: The probability that a randomly chosen applicant is male given that the applicant has a graduate degree is 0.5895 or 58.95%.

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