Data Sufficiency

AAPL wrote:Manhattan Prep

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

Target question: What is the probability that Katelyn wins at least one of the 3 games?
This is a good candidate for rephrasing the target question.
In order to determine P(Katelyn wins at least one of the 3 games), we need to know the probability that Katelyn wins if they play ONE game.
We can then use that information to determine the probability of her winning at least one of 3 games

REPHRASED target question: What is the probability that Katelyn wins if they play ONE game?

Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Statement 1: The probability that either James or Austin wins the game is 3/4.
Use the complement to write: P(Katelyn wins) = 1 - P(Katelyn DOESN'T win)
Notice that, if Katelyn DOESN'T win, then EITHER James wins OR Austin wins
In other words, P(Katelyn DOESN'T win) = P(James wins or Austin wins)
Statement 1 tells us that P(James wins or Austin wins) = 3/4
So, P(Katelyn DOESN'T win) = 3/4
So, P(Katelyn wins) = 1 - 3/4 = 1/4
So, the answer to the REPHRASED target question is P(Katelyn wins) = 1/4
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: James and Katelyn have an equal probability of winning the game.
Key Concept: If the 3 people play one game, then P(James wins) + P(Austin wins) + P(Katelyn wins) = 1
There are infinitely many scenarios that satisfy statement 2. Here are two:
Case a: P(James wins a game) = 0.3, P(Katelyn wins a game) = 0.3 and P(Austin wins a game) = 0.4 . In this case, the answer to the REPHRASED target question is P(Katelyn wins) = 0.3
Case b: P(James wins a game) = 0.2, P(Katelyn wins a game) = 0.2 and P(Austin wins a game) = 0.6 . In this case, the answer to the REPHRASED target question is P(Katelyn wins) = 0.2
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent