Question

The probability that a person is accepted for admission to a specific university is 0.6. Determine the probability that exactly two of the next five people who apply to that university get accepted.

Answer 1

0.2304 or 23.04%

Explanation:

Please kindly check the attached files for explanation

Answer 2

Answer: the probability that exactly two of the next five people who apply to that university get accepted is 0.23

Explanation:

We would number of people that applies for admission at the university and gets accepted. The formula is expressed as

P(x = r) = nCr × p^r × q^(n - r)

Where

x represent the number of successes.

p represents the probability of success.

q = (1 - p) represents the probability of failure.

n represents the number of trials or sample.

From the information given,

p = 0.6

q = 1 - p = 1 - 0.6

q = 0.4

n = 5

the probability that exactly two of the next five people who apply to that university get accepted is

P(x = 2) = 5C2 × 0.6^2 × 0.4^(5 - 2)

P(x = 2) = 10 × 0.36 × 0.064

P(x = 2) = 0.23