Question

According to a survey of 95,845 first-time freshmen enrolled at four-year colleges, 52,163 reported that they were enrolled at their first-choice college. (a) if a person who participated in this survey is selected at random, what is the probability that the selected person was enrolled at their first-choice college? (round your answer to four decimal places.) (b) what is the probability that the selected person was not enrolled at their first-choice college? (round your answer to four decimal places.)

Answer 1

The probability that a randomly selected person was enrolled at their first-choice college is 0.5447, while the probability that they were not enrolled at their first-choice college is 0.4553.

Step-by-step explanation:

To calculate the probability that a person selected at random was enrolled at their first-choice college, we need to divide the number of people enrolled at their first-choice college by the total number of participants in the survey. From the given information, we know that 52,163 out of 95,845 first-time freshmen reported being enrolled at their first-choice college. So, the probability is:

P(enrolled at first-choice college) = 52,163 / 95,845 = 0.5447 (rounded to four decimal places)

To calculate the probability that a person selected at random was not enrolled at their first-choice college, we can subtract the probability of being enrolled from 1, since these are the only two possibilities. So, the probability is:

P(not enrolled at first-choice college) = 1 - P(enrolled at first-choice college) = 1 - 0.5447 = 0.4553 (rounded to four decimal places)