Question

Three girls (Brooke, jessie, and Zoey) are going to have a friendly chess tournament, Only one girl can win, and it is known that jessie is five times as likely to win the tournament as Brooke.

while Brooke is one third as likely as Zoey to win. Determine the probability that Zoey turns out to win the chess toumament.
A. 1/3
B. 2/3
C. 4/9
D. 5/9

Answer 1

To determine the probability that Zoey wins the chess tournament, we need to use the given information about the likelihood of each person winning. By representing the probabilities of each person winning and using the equation that the sum of the probabilities is equal to 1, we can solve for the probability of Zoey winning. The probability that Zoey wins the chess tournament is 1/3.

Step-by-step explanation:

To determine the probability that Zoey wins the chess tournament, we need to use the information given about the likelihood of each person winning. Let's assign variables to represent the probabilities: P(J) for Jessie, P(B) for Brooke, and P(Z) for Zoey. It is given that P(J) = 5 * P(B) and P(B) = 1/3 * P(Z). We also know that only one person can win, so the sum of the probabilities must be equal to 1: P(J) + P(B) + P(Z) = 1.

Substituting the given information into this equation, we can solve for P(Z). Since P(B) = 1/3 * P(Z), we can rewrite the equation as follows: 5 * P(B) + P(B) + P(Z) = 1. Combining the like terms, we get 6 * P(B) + P(Z) = 1. Substituting P(B) = 1/3 * P(Z), we get 6 * (1/3 * P(Z)) + P(Z) = 1. Simplifying further, we have 2 * P(Z) + P(Z) = 1.

Combining like terms and simplifying again, we get 3 * P(Z) = 1. Dividing both sides by 3, we find that P(Z) = 1/3. Therefore, the probability that Zoey wins the chess tournament is 1/3, which corresponds to option A.