Question

the accompanying table shows the numbers of male and female students in a particular country who received bachelors degrees in business in a recent year. complete parts (a) and (b) below.
click the icon to view the data on business degrees.
(a) find the probability that a randomly selected student is male, given that the student received a business degree.
the probability that a randomly selected student is male, given that the student received a business degree, is 0.529
(round to three decimal places as needed.)
(b) find the probability that a randomly selected student received a business degree, given that the student is female.
the probability that a randomly selected student received a business degree, given that the student is female, is
(round to three decimal places as needed.)
business graduates
male: business degrees 192,480; nonbusiness degrees 633,059; total 825,539
female: business degrees 171,281; nonbusiness degrees 940,321; total 1,111,602
total: business degrees 363,761; nonbusiness degrees 1,573,380; total 1,937,141

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). In the context of part (b), let \(A\) be the event that a student received a business degree and \(B\) be the event that a student is female. So \(P(A|B)=\frac{\text{Number of female - business degree students}}{\text{Total number of female students}}\).

Step2: Identify the relevant values from the table

From the table, the number of female students who received a business degree (\(n_{F - B}\)) is \(171,281\), and the total number of female students (\(n_F\)) is \(1,111,602\).

Step3: Calculate the probability

$$P=\frac{171281}{1111602}\approx 0.154$$

Answer:

\(0.154\)