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 (round to three decimal places as needed.) business graduates male female total business degrees 188,541 161,130 349,671 nonbusiness degrees 634,749 887,790 1,522,539 total 823,290 1,048,920 1,872,210

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability \(P(A|B)=\frac{P(A\cap B)}{P(B)}\). In the context of this problem, if \(A\) is the event that the student is male and \(B\) is the event that the student received a business degree, then \(P(A|B)=\frac{\text{Number of male business - degree recipients}}{\text{Total number of business - degree recipients}}\)

Step2: Identify the relevant values from the table

From the table, the number of male business - degree recipients \(n(\text{Male}\cap\text{Business}) = 188541\), and the total number of business - degree recipients \(n(\text{Business})=349671\)

Step3: Calculate the probability

\(P=\frac{188541}{349671}\approx0.539\)

Answer:

\(0.539\)