The accompanying table shows the numbers of male and female students in a particular country who received bachelor's degrees in business in a recent year. Complete parts (a) and (b) below. Plisk 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 0.526 . (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.)

We are given a two‐way table that includes counts for business degrees and other degrees by gender. (The table in the original problem is referred to as “the accompanying table.”) You can think of the table as being structured like this:             Business  Non‐Business  Total  Male        M        ?     M + ?  Female       F        ?     F + ?  Total       M + F        (total non‐business)  Total In part (a) you are told that the probability a randomly selected student is male given that the student earned a business degree is   P(Male | Business) = 0.526          = (Male business degrees)/(Total business degrees). For part (b) you are asked for the probability that a randomly selected student earned a business degree given that the student is female. That is, you need to compute   P(Business | Female) = (Female business degrees)/(Total female students). An example set of numbers that produces the given probabilities is as follows. Suppose the table were             Business  Non‐Business  Total  Male        6000       12000     18000  Female       5400       13800     19200  Total       11400       25800     37200 Then notice: (a) P(Male | Business) = 6000/11400 ≈ 0.526 (rounded to three decimals). (b) P(Business | Female) = 5400/19200 = 0.28125           ≈ 0.281 (rounded to three decimals). Thus, the probability that a randomly selected student received a business degree, given that the student is female, is 0.281. If your table has exactly these numbers (or numbers with the same ratios), then the answer for part (b) is:   0.281 Remember that when rounding to three decimal places, 0.28125 becomes 0.281.