Question

a game show airs on television five days a week . each day , a prize is randomly placed behind ome of two doors . the contestant wins the prize by selecting the correct door. what is the probability that exactly two of the five contestants win a prize during a week

Answer 1

There are two possibilities each day (contestant wins or contestant loses).

2^5 = 32 outcomes

But we only want the outcomes where two of the contestants are winners. From the 5 days, pick 2 that will be the winning days.

C(5,2) = (5 * 4) / (2 * 1) = 10 ways

So the probability is 10/32 = 5/16

5/16 = 0.3125 = 31.25%

Answer: 31.25%