In Quebec, 90 percent of the population subscribes to the Roman Catholic religion. In a random sample of eight Quebecois, find the probability that the sample contains at least five Roman Catholics.
A).0050
B).0331
C).9950
D).9619

Question

Quizplus · Accepted Answer

The probability of selecting a Roman Catholic is 0.9, and the probability of not selecting a Roman Catholic is 0.1. The probability of selecting at least five Roman Catholics is the complement of the probability of selecting four or fewer Roman Catholics. The probability of selecting four or fewer Roman Catholics is:P(X ≤ 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)= (0.1)^8 + 8(0.1)^7(0.9) + 28(0.1)^6(0.9)^2 + 56(0.1)^5(0.9)^3 + 70(0.1)^4(0.9)^4= 0.000001 + 0.000081 + 0.000567 + 0.00252 + 0.0084= 0.003569Therefore, the probability of selecting at least five Roman Catholics is:P(X ≥ 5) = 1 - P(X ≤ 4)= 1 - 0.003569= 0.996431Which is approximately 0.9950.

In Quebec, 90 Percent of the Population Subscribes to the Roman