Suppose that one-half of the new buildings in a town are in violation of the building code. If a building inspector inspects seven of the buildings, find the probability that the first five buildings will pass the inspection and the remaining two will fail the inspection. Then find the probability that just five of the buildings will pass inspection.

Question

Suppose that one-half of the new buildings in a town are in violation of the building code. If a building inspector inspects seven of the buildings, find the probability  that the first five buildings will pass the inspection and the remaining two will fail the inspection. Then find the probability  that just five of the buildings will pass inspection. ​

Quizplus · Accepted Answer

The probability that the first five buildings pass inspection is (1/2)^5 = 1/32. The probability that the remaining two fail inspection is (1/2)^2 = 1/4. Therefore, the probability that the first five pass and the remaining two fail is (1/32) * (1/4) = 1/128. To find the probability that just five of the buildings pass inspection, we need to consider all the possible arrangements of passing and failing buildings in the seven that were inspected. There are (7 choose 5) = 21 such arrangements. Each of these arrangements has a probability of (1/2)^7 = 1/128 of occurring. Therefore, the overall probability of just five passing is 21/128. The closest choice is therefore B.

Suppose That One-Half of the New Buildings in a Town