Question

A striking trend in higher education is that more women than men reach each level of attainment. The National Center for Educational Statistics provides projections for the number of degrees earned, classified by level and by the sex of the degree recipient. Here are the projected number of earned degrees (in thousands) in the United States for an academic year.
Associates Bachelors Masters Doctorate Total
female 603 1063 494 97 2257
male 359 804 326 85 1574
total 962 1867 820 182 3831
(a) If you choose a degree recipient at random, what is the probability that the person you choose is a man? (Round your answer to 4 decimal places.)
(b) What is the conditional probability that you choose a man, given that the person chosen received a master's? (Round your answer to 4 decimal places.)

Answer 1

Answer:

See the explanation.

Step-by-step explanation:

(a)

Total number of degree recipients are 3831.

From 3831 recipients, 1 can be chosen in $^{3831}C_1 = 3831$ ways.

Among the 3831 recipients, total number of male is 1574.

Similar as above, 1 male can be chosen in 1574 ways.

Hence, the probability of the chosen person being a male is $\frac{1574}{3831} = 0.4108587$ ≅ 0.4109.

(b)

Total males are 1574 in number.

Among them 326 males have done masters.

The probability of the chosen male has done masters is $\frac{326}{1574} = 0.2071156$ ≅ 0.2071.