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
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In a certain game only one player can win and only one playe
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BTGmoderatorDC
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Probability that Katelyn wins at least one of the 3 gamesBTGmoderatorDC wrote: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
= 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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