Question

Out of 400 applicants for a job, 184 are male and 78 are male and have a graduate degree. Step 1 of 2: What is the probability that a randomly chosen applicant has a graduate degree, given that they are male? Express your answer as a fraction or a decimal rounded to four decimal places. Step 2 of 2: If 125 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.

Answer 1

Answer:

Step 1

$P = 0.4239$

Step 2

$P = 0.624$

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this problem, we have that:

There are 400 applicants for a job

184 are male

78 are male and have a graduate degree.

Step 1 of 2: What is the probability that a randomly chosen applicant has a graduate degree, given that they are male? Express your answer as a fraction or a decimal rounded to four decimal places.

Desired outcomes:

Number of male applicants with a graduate degree, which is 78

Total outcomes:

Number of male applicants, which is 184

Probability:

$P = \frac{78}{184} = 0.4239$

Step 2 of 2: If 125 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.

Desired outcomes:

Number of male applicants with a graduate degree, which is 78

Total outcomes:

Number of applicants with graduate degrees, which is 115

Probability:

$P = \frac{78}{125} = 0.624$