Question

In a survey of 300 college graduates, 46% reported that they entered a profession closely related to their college major. If 9 of those survey subjects are randomly selected without replacement for a follow-up survey, what is the probability that 3 of them entered a profession closely related to their college major?

a) 0.0973
b) 0.203
c) 0.797
d) 0.102

Answer 1

The probability that exactly 3 out of 9 randomly selected college graduates entered a profession related to their college major is 0.203 (b). The calculation is based on the binomial distribution formula.

Step-by-step explanation:

The student's question involves calculating the probability that 3 of the 9 randomly selected college graduates entered a profession related to their college major based on an initial survey of 300 graduates where 46% reported so. This can be modeled as a hypergeometric probability problem, but it resembles a binomial distribution since we are dealing with a large population and a small sample. The probability of exactly 3 out of 9 graduates reporting this can be calculated using the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

Where:

• n is the number of trials (9 graduates)
• k is the number of successes (3 graduates)
• p is the probability of success on any given trial (0.46)

Applying this to the binomial formula, we find:

P(3) = (9 choose 3) * 0.46^3 * (1-0.46)^6

After calculations, it can be determined that the closest answer provided by the options is 0.203, so choice b) 0.203 is correct.