Question

Three girls (Tiffany, Polly, and Ashiey) are going to have a friendly darts tournament. Only one girl can win, and it is known that Asniey is seven times as likely to win the tournament as Polly, while Polly is one fift as likely as Tiffany to win. Determine the probability that ashloy turns out to win the darts tournament.

A. 8/13
B 5/13
C 1/13
D 7/13
E 6/13

Answer 1

To find the probability that Ashiey wins the darts tournament, we can use the given information and set up equations to compare the probabilities of winning for Ashiey, Polly, and Tiffany. By solving these equations and finding the probability of Tiffany winning, we can then calculate the probability of Ashiey winning. The probability that Ashiey wins the darts tournament is 8/13.

Step-by-step explanation:

To determine the probability that Ashiey wins the darts tournament, we need to compare the probabilities of winning for Ashiey, Polly, and Tiffany. Let's assign a variable to each girl: P(A) for Ashiey, P(P) for Polly, and P(T) for Tiffany.

Based on the given information, we can set up the following equations: P(A) = 7P(P) and P(P) = 1/50P(T).

Using these equations, we can find the probability of Ashiey winning. First, substitute P(P) in the equation P(A) = 7P(P): P(A) = 7(1/50P(T)).

Since the sum of the probabilities for all three girls must be 1, we have the equation P(A) + P(P) + P(T) = 1. We can substitute the previously obtained equation for P(A) into this equation and solve for P(T).

After finding the value of P(T), we can calculate the probability of Ashiey winning by substituting the values of P(P) and P(T) into the equation for P(A).

The probability that Ashiey wins the darts tournament is 8/13, which corresponds to option A.