In a certain game only one player can win and only one playe

[BTGmoderatorDC]

In a certain game only one player can win and only one player always eventually wins. James, Austin, and Katelyn play this game together 3 times in a row. What is the probability that Katelyn wins at least one of the 3 games.?

(1) The probability that either James or Austin wins the game is 3/4
(2) James and Katelyn have an equal probability of winning the game.

OA A

Source: Manhattan Prep

[Jay@ManhattanReview]

In a certain game only one player can win and only one player always eventually wins. James, Austin, and Katelyn play this game together 3 times in a row. What is the probability that Katelyn wins at least one of the 3 games.?

(1) The probability that either James or Austin wins the game is 3/4
(2) James and Katelyn have an equal probability of winning the game.

OA A

Source: Manhattan Prep

Probability that Katelyn wins at least one of the 3 games

= 1 - (Probability that Katelyn loses all the 3 games)
= 1 - (Probability that either James or Austin wins all the 3 games)

Let's take each statement one by one.

(1) The probability that either James or Austin wins the game is 3/4

=> Probability that either James or Austin wins all the 3 games = (3/4)^3

Thus, the probability that Katelyn wins at least one of the 3 games = 1 - (3/4)^3

Sufficient.

(2) James and Katelyn have an equal probability of winning the game.

It does not help in getting the unique answer. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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