In a certain office, six men determine who will pay for coffee by each flipping a coin. If one of them has an outcome that is different from the other five, he must pay for the coffee. What is the probability that in any play of the game there will be an "odd man out"?
A) 0.1875
B) 0.1125
C) 0.0188
D) 0.1313
E) 0.0750

Question

In a certain office, six men determine who will pay for coffee by each flipping a coin. If one of them has an outcome that is different from the other five, he must pay for the coffee. What is the probability that in any play of the game there will be an "odd man out"? ​
A) 0.1875
B) 0.1125
C) 0.0188
D) 0.1313
E) 0.0750

Quizplus · Accepted Answer

The probability of having an "odd man out" is calculated by considering two scenarios: one man gets tails (and the others get heads) or one man gets heads (and the others get tails). The probability for one scenario (e.g., one man gets tails) is $6 \times \left(\frac{1}{2}\right)^6 = \frac{6}{64} = \frac{3}{32}$. Since there are two such scenarios, the total probability is $2 \times \frac{3}{32} = \frac{6}{32} = \frac{3}{16} = 0.1875$.

In a Certain Office, Six Men Determine Who Will Pay