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If a jury of 12 people is to be selected randomly from a pool of 15 po
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31 Mar 2021, 05:00
31 Mar 2021, 05:00
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If a jury of 12 people is to be selected randomly from a pool of 15 potential jurors, and the jury pool consists of 2/3 men and 1/3 women, what is the probability that the jury will comprise at least 2/3 men?
A. 24/91
B. 45/91
C. 2/3
D. 67/91
E. 84/91
A. 24/91
B. 45/91
C. 2/3
D. 67/91
E. 84/91
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If a jury of 12 people is to be selected randomly from a pool of 15 po
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31 Mar 2021, 07:35
31 Mar 2021, 07:35
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GeminiHeat wrote:
If a jury of 12 people is to be selected randomly from a pool of 15 potential jurors, and the jury pool consists of 2/3 men and 1/3 women, what is the probability that the jury will comprise at least 2/3 men?
A. 24/91
B. 45/91
C. 2/3
D. 67/91
E. 84/91
A. 24/91
B. 45/91
C. 2/3
D. 67/91
E. 84/91
Total jurors = \(15\)
Men = \(\frac{2}{3}(15) = 10\)
Women = \(15 - 10 = 5\)
Jury = \(12\)
Men (at-least) = \(\frac{2}{3}(12) = 8\)
Case I: 8M4W
possible selections = \((^{10}C_8)(^5C_4) = 225\)
Case II: 9M3W
possible selections = \((^{10}C_9)(^5C_3) = 100\)
Case III: 10M2W
possible selections = \((^{10}C_{10})(^5C_2) = 10\)
Total possibilities of selecting \(12\) members from \(15\) = \(^{15}C_{12} = 455\)
Required probability = \(\frac{(225 + 100 + 10)}{455} = \frac{335}{455} = \frac{67}{91}\)
Hence, option D
gmatclubot
If a jury of 12 people is to be selected randomly from a pool of 15 po [#permalink]
31 Mar 2021, 07:35
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