Question

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

Answer 1

The odds in favor of the Cougars winning the toss in exactly two of three games is 3:5 as calculated by determining the probabilities of all combinations where they win twice and lose once.

Step-by-step explanation:

To calculate the odds in favor of the Cougars winning the toss in exactly two of three games, we consider that each toss of a coin has two possible outcomes: heads (H) or tails (T) with an equal probability of 1/2 each. We are interested in scenarios where they win twice and lose once. These scenarios are (HHT), (HTH), and (THH). The probability for each of these scenarios is ((1/2) * (1/2) * (1/2)), and since there are three such scenarios, the total probability of winning exactly two tosses is 3 * (1/2 * 1/2 * 1/2) = 3/8.

The odds in favor of an event are given by the ratio of the probability of the event happening to the probability of it not happening. Thus, the odds in favor of the Cougars winning exactly two out of three coin tosses are 3/8 (winning) to 5/8 (not winning), which simplifies to 3:5 (Answer A).

Answer 2

in irder to solve this problem

we need to now that the probability to win one coin toss is 0.5

so other thing we need to know is

there all these possible scenarios that will happen

w= win

L=lose

WWW

WWL

WLW

LWW

LLW

LWL

LLW

LLL

as you can see only in 3 scenarios when the cougar win exactly 2

so the correct answer is B