Question

The probability of a student passing math is 20%. What is the probability that if three students are selected at random, only one student passes math?

(A) 0.512
(B) 0.384
(C) 0.096
(D) 0.008

Answer 1

The probability that only one student passes math out of three random students is 0.384

Step-by-step explanation:

To find the probability that only one student passes math out of three random students, we need to use the binomial probability formula. The formula is:

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

Where X is the number of successes, n is the number of trials, p is the probability of success, and k is the specific number of successes we want to calculate the probability for.

In this case, X=1, n=3, and p=0.2. Plugging these values into the formula gives:

P(X=1) = C(3,1) * 0.2^1 * (1-0.2)^(3-1) = 3 * 0.2 * 0.8^2 = 0.384

Therefore, the probability that only one student passes math is 0.384. The correct answer choice is (B) 0.384.