Question

As part of a promotional campaign, a gas station hands out game pieces to customers at a rate of one per visit. Each piece has a letter or an exclamation point on it, and if you collect all seven game pieces they spell you win! If you've collected six of the seven game pieces, and all you need is the letter w to get all seven, what's the probability you'll get your piece on the fifth trip to the gas station? Assume there are equal numbers of each piece.

A. (1/7) + (6/7)(1/7) + (6/7) ^ 2 * (1/7) + (6/7) ^ 3 * (1/7) + (6/7) ^ 4 * (1/7)

D. (1/7) + (6/7)(1/7) + (6/7) ^ 2 * (1/7) + (6/7) ^ 3 * (1/7) + (6/7) ^ 4 * (1/7) (6/7) deg * (1/7)

E. (1/7) + (6/7)(1/7) + (6/7) ^ 2 * (1/7)

B. (6/7) ^ 4 * (1/7)

C. 5 * (6/7) ^ 4 * (1/7)

Answer 1

The correct answer is B. (6/7) ^ 4 * (1/7)

On the fifth trip to the gas station, you will have already made 4 trips without getting the letter w. The probability of not getting the letter w on each trip is 6/7, so the probability of not getting the letter w on all 4 trips is (6/7) ^ 4.

Therefore, the probability of getting the letter w on the fifth trip is (6/7) ^ 4 * (1/7).