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If a jury of 12 people is to be selected randomly from a

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Senior Manager
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Joined: 08 Dec 2015
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GMAT 1: 600 Q44 V27
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If a jury of 12 people is to be selected randomly from a [#permalink]

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New post 08 Jun 2016, 08:41
A guessing strategy from Magoosh:

When you see that the problem can be solved using the 1-(P of opposite), in this case 1-(P of 5 women being selected), find two choices among the answers that added together yield 1. (no calculations what so ever, just the addition of any two answers must have 1 as result)

In this case its A and D. No other answers combo gives you 1 as result of addition.

When you subtract 24/91 from 1 you get 67/97, so the final answer. And we are looking for these "pairs" in the answer choices.

The P(5 women being selected) is a trap answer for those who forget to subtract that from 1. So the existence of these trap-answers that are supposed to confuse you allows you to use this strategy on a well-designed, typical GMAT question.

Then you have a 50% guess or:

see that you have a +- 33% chance (A) and a +-66% chance (D) choices. You can reason that the nº of men is quite large so its likely that the jury will be comprised mostly of men. so D looks like a good guess.

Thanks to Magoosh ;)
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Concentration: Marketing, International Business
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GMAT 1: 770 Q51 V44
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Re: If a jury of 12 people is to be selected randomly from a [#permalink]

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New post 07 Jan 2017, 08:30
Approach 1:-



Another way to solve this is "1-x" prob shortcut.
We need to know what is the probability of 7 men in jury, since it is the only way there are fewer than 8 men in jury ( maximum number of women is 5 ==> so 12-5=7 must be men). Then you have to 1-prob.of.7men.

1) All possible ways to assemble jury are : 15!/12!3!=455.
2) 7 of 10 men : 10!/7!3!=120
3) and the only way to include all women in jury is 5!/5!=1.

All possible ways to assemble 7men-5women jury will be 120*1=120.
Then, 120/455=24/91 - is the probability of 7 men and 5 woman in jury.
Hence, the probability that there will be more than 7 men in the jury is (1 - 24/91)=67/


Approach 2:-


there are total 10 men and 5 women
in 12 jury members, could be:

M W T
10+2=12
9+3=12
8+4=12
7+5=12
M-men , W-women T - total

So out of 4 possible outcomes 3 are favourbale, 1 is unfavorable, it is 3/4=0.75

67/91~73%., which is the closest to 3/4.
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Anaira Mitch

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Re: If a jury of 12 people is to be selected randomly from a [#permalink]

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New post 14 Jan 2018, 10:47
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Re: If a jury of 12 people is to be selected randomly from a   [#permalink] 14 Jan 2018, 10:47

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