Question

Question: Suppose in a recent year, there were 8 million male undergraduates in the United States and 11 million female undergraduates. Suppose that, among males, 61.6% received financial aid and 38.4% did not receive financial aid. Further, among female, 66.2% received financial aid and 33.8% did not receive financial aid. (a) Suppose we select one randomly selected

Suppose in a recent year, there were 8 million male undergraduates in the United States and 11 million female undergraduates. Suppose that, among males, 61.6% received financial aid and 38.4% did not receive financial aid. Further, among female, 66.2% received financial aid and 33.8% did not receive financial aid. (a) Suppose we select one randomly selected undergraduate. What is the probability that the undergraduate is a male student without financial aid? (b) What proportion of all undergraduates receive financial aid? 1 (c) Suppose we select one randomly selected undergraduate who receives financial aid. What is the probability that this is a male student?

Answer 1

To find the probability of selecting a male student without financial aid, you multiply the total number of male undergraduates by the percentage without financial aid and divide it by the total number of undergraduates. To determine the proportion of undergraduates who receive financial aid, add the financially aided students from both genders and divide by the total number of undergraduates. To calculate the probability that a financially aided undergraduate is male, divide the number of aided male students by the total aided students.

Step-by-step explanation:

The probability that the undergraduate is a male student without financial aid:

First, we calculate the number of male students without financial aid by multiplying the total number of male undergraduates by the percentage that did not receive financial aid: 8 million × 38.4% = 3.072 million.

Next, we find the total number of undergraduates by adding the number of male and female undergraduates: 8 million + 11 million = 19 million.

Then, we divide the number of male students without financial aid by the total number of undergraduates to find the probability: 3.072 million / 19 million ≈ 0.1617 or 16.17%.

The proportion of all undergraduates that receive financial aid:

Males receiving financial aid: 8 million × 61.6% = 4.928 million.

Females receiving financial aid: 11 million × 66.2% = 7.282 million.

Total receiving financial aid: 4.928 million + 7.282 million = 12.21 million.

The proportion is found by dividing the number of students receiving aid by the total number of students: 12.21 million / 19 million ≈ 0.6426 or 64.26%.

The probability that a randomly selected undergraduate who receives financial aid is a male student:

We've already calculated the number of males receiving financial aid (4.928 million) and the total number receiving financial aid (12.21 million).

Divide the males receiving financial aid by the total receiving financial aid: 4.928 million / 12.21 million ≈ 0.4035 or 40.35%.