Question

You're playing a game in which the probability of winning each round is .20. On average, how many rounds do you have to play to first win?

A. 20
B. 10
C. 15
D. 5
E. .5

Answer 1

On average, you would have to play 2 rounds to win.

Step-by-step explanation:

To determine the number of rounds on average that you have to play to first win, you can use the concept of expected value.

The probability of winning each round is 0.20, so the probability of losing each round is 0.80.

The expected value is calculated by dividing the probability of winning once by the probability of losing once, which in this case is 0.20 divided by the complement of 0.20 (1 - 0.20).

Expected value = 1 / 0.80 = 1.25

Therefore, on average, you would have to play 1.25 rounds to win. Since you cannot play a fraction of a round, the answer would be rounded up to the nearest whole number, which is 2.