A club has nine members. One member starts a rumor by telling it to a second club member, who repeats the rumor to a third member, and so on. At each stage, the recipient of the rumor is chosen at random from the nine club members. What is the probability that the rumor will be told eight times without returning to the originator? Round to the nearest hundredth.
A)0.49
B)0.44
C)0.55
D)0.70
E)0.79

Question

Quizplus · Accepted Answer

The probability that the rumor will be told eight times without returning to the originator can be calculated by considering the choices available at each stage. Initially, the rumor can be passed to any of the 8 remaining members (since the originator cannot be chosen). After the first pass, the rumor can be passed to any of the 7 remaining members (excluding the originator and the current holder), and so on. Thus, the probability is calculated as the product of the probabilities at each stage: (8/8) * (7/8) * (6/7) * (5/6) * (4/5) * (3/4) * (2/3) * (1/2) = 1/8, which when rounded to the nearest hundredth is approximately 0.44.

A Club Has Nine Members