binomial probability

Question

of all college freshman who try out for the track team, the coach will only accept 25%. if 14 freshman try out for the track team, what is the probability that:

a. none of the 14 are accepted

b. at least 5 are accepted

c. no more than 3 are accepted

d. between 2 and 7 are accepted (including 2 and 7)

Answer 1

formula for binomial probability:

probability x successes in n independent trials, where each trial has the probability p of success:

P(x;n;p) = n!

---- * p^x * (1-p)^(n-x)

x!(n-x)!

For these problems p = 0.25 and n = 14

a. none of the 14 are accepted

use formula to compute probability for x = 0

b. at least 5 are accepted

compute probability for x = 0, 1, 2, 3 and 4. Sum probabilities and subtract from 1.

c. no more than 3 are accepted

compute probability for x = 0, 1, 2 and 3. Sum probabilities.

d. between 2 and 7 are accepted (including 2 and 7)

compute probability for x = 2, 3, 4, 5, 6 and 7. Sum probabilities.