Question

Of all college freshmen who try out for the track team, typically only 30% make it. If 10 freshmen try out for the track team, what is the probability that

(a) all 10 are accepted?
(b) at least 5 are accepted?
(c) no more than 3 are accepted?
(d) between 5 and 10 are accepted (including 5 and 10)?"

Answer 1

The probability that all 10 freshmen are accepted is approximately 0.000005. The probability that at least 5 freshmen are accepted is approximately 0.996. The probability that no more than 3 freshmen are accepted is approximately 0.653. The probability that between 5 and 10 freshmen are accepted is approximately 0.995.

Step-by-step explanation:

a) Probability that all 10 are accepted:

Since the probability of a freshman being accepted is 30% or 0.3, the probability of all 10 freshmen being accepted is (0.3)^10, which is equal to approximately 0.000005.

b) Probability that at least 5 are accepted:

The probability of at least 5 freshmen being accepted can be found by adding the probabilities of 5, 6, 7, 8, 9, and 10 freshmen being accepted. Each individual probability can be calculated using the binomial probability formula. Summing up these probabilities, we get approximately 0.996.

c) Probability that no more than 3 are accepted:

The probability of no more than 3 freshmen being accepted can be found by adding the probabilities of 0, 1, 2, and 3 freshmen being accepted. Each individual probability can be calculated using the binomial probability formula. Summing up these probabilities, we get approximately 0.653.

d) Probability that between 5 and 10 are accepted:

The probability of between 5 and 10 freshmen being accepted can be found by subtracting the probability of no more than 4 freshmen being accepted from the probability of no more than 10 freshmen being accepted. Each individual probability can be calculated using the binomial probability formula. The result is approximately 0.995.