Question

According to student loan company Sallie May, 85% of college students had credit cards in 2008, Answer this question based on a random sample of 6 students?

a) What is the probability that all 6 have credit cards?

b) What is the probability that 4 or more have credit cards?

Answer 1

a)

Here, n = 6, p = 0.85, (1 - p) = 0.15 and x = 6
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 6)
P(X = 6) = 6C6 * 0.85^6 * 0.15^0
P(X = 6) = 0.3771

b)

Here, n = 6, p = 0.85, (1 - p) = 0.15 and x = 4
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X >= 4).
P(X >= 4) = (6C4 * 0.85^4 * 0.15^2) + (6C5 * 0.85^5 * 0.15^1) + (6C6 * 0.85^6 * 0.15^0)
P(X >= 4) = 0.1762 + 0.3993 + 0.3771
P(X >= 4) = 0.9526