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Team A has a 50% chance of winning any game that it plays. Team B has

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Carcass
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Team A has a 50% chance of winning any game that it plays. Team B has [#permalink] New post   18 Mar 2021, 02:40
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Team A has a 50% chance of winning any game that it plays. Team B has a 60% chance of winning any game that it plays.

Quantity A
Quantity B
The probability that Team A will win its next three games in a row
The probability that Team B will win its next four games in a row



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

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Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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KarunMendiratta
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Team A has a 50% chance of winning any game that it plays. Team B has [#permalink] New post   18 Mar 2021, 06:53
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Carcass wrote:
Team A has a 50% chance of winning any game that it plays. Team B has a 60% chance of winning any game that it plays.

Quantity A
Quantity B
The probability that Team A will win its next three games in a row
The probability that Team B will win its next four games in a row



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.


\(P(A) = 0.5\)
\(P(B) = 0.6\)

Col. A: \((0.5)(0.5)(0.5) = \frac{125}{1000}\)
Col. B : \((0.6)(0.6)(0.6)(0.6) = \frac{1296}{10000}\)

Cross-multiply the denominators:

Col. A: \(1250\)
Col. B : \(1296\)

Hence, option B
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Team A has a 50% chance of winning any game that it plays. Team B has [#permalink] New post   18 Mar 2021, 11:01
I found it easier to solve by converting everything to fraction form.

QA: (1/2)(1/2)(1/2) = 1/8

QB: (3/5)(3/5)(3/5)(3/5) = 81/625, or approximately .129

.129 > .125 (the decimal form of 1/8), so QB is greater.
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Re: Team A has a 50% chance of winning any game that it plays. Team B has [#permalink] New post   24 Mar 2021, 04:55
Probability of team A winning 3 games continuously= \((0.5)^3\) = 0.1250

Probability of team B winning 4 games continuously= \((0.6)^4\) = 0.1296

Hence Option B is correct
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Re: Team A has a 50% chance of winning any game that it plays. Team B has [#permalink]
24 Mar 2021, 04:55
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