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Probability

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Probability

by svishal1123 » Sat Apr 25, 2009 10:04 pm
Need help with this question

If 2 different representatives are to be selected at random from a group of 10 employees and if p is the probability that both representatives selected will be women, is p > 1/2?

(1) More than 1/2 of the 10 employees are women.
(2) The probability that both representatives selected will be men is less than 1/10
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Source: — Data Sufficiency |
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by Feep » Sun Apr 26, 2009 12:55 am
(1) states that anywhere from 6 to 10 of the employees are women. Let's look at both extremes: if it is 6, the probability that both will be selected is (6/10) * (5/9) = 30/90 = 1/3, less than 1/2.

If it is 10, the probability that both will be selected is 100%, of course. Since we can yield two different answers for "is p > 1/2", this is insufficient.

(2) states that the probability that both will be men is less than 10%. We note that 0 and 1 man is obviously satisfactory, 2 men is (2/10) * (1/9) = 2 / 90 = 1/45, easily satisfactory, and (3/10) * (2/9) = 6 / 90 = 1/15, satisfactory. 4 men, however, yields (4/10) * (3/9) = 12/90, which is greater than 10%.

So, this statement is essentially saying, the number of men is between 0-3, or rather, the number of women is between 7 and 10. We've already tested 10, how about 7? (7/10) * (6/9) = 42/90, less than 1/2. Darn. This range is insufficient, as 7 women and 10 women yield different answers to the problem.

(1) and (2) together don't narrow the range, however. (1) ranged from 6-10 women, (2) ranged from 7-10. Together, the range is still 7-10. No dice.

Wholly insufficient. E.
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