Question

A coin toss is used to determine which team will receive the ball at the beginning of a football game. The Red Lakers always choose heads in the toss. What are the odds in favor of the Lakers winning the toss in exactly one of three games?
A. 5:3
B. 3:5
C. 3:8
D. 8:3

Answer 1

The probability of the Red Lakers winning the coin toss in one game is 1/2, since there are two possible outcomes (heads or tails) and the Red Lakers always choose heads.

The probability of the Red Lakers winning the coin toss in exactly one of three games can be calculated using the binomial probability formula:

P(exactly one win) = (number of ways to win once) x (probability of winning) x (probability of losing)^(number of losses)

The number of ways to win once in three games is 3 (since the win could occur in the first, second, or third game). The probability of winning once is 1/2, and the probability of losing twice is (1/2)^2 = 1/4.

Therefore, P(exactly one win) = 3 x (1/2) x (1/4)^(2) = 3/8.

This means that the odds in favor of the Red Lakers winning the coin toss in exactly one of three games are 3:5, since there are 3 favorable outcomes (winning once) to 5 unfavorable outcomes (winning zero or winning twice).

So, the answer is B. 3:5.