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GMAT prep - Probability DS

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GMAT prep - Probability DS

by [email protected] » Tue Sep 04, 2007 5:39 pm
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 > 21?
(1) More than 21 of the 10 employees are women.
(2) The probability that both representatives selected will be men is less than 101.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
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Source: — Data Sufficiency |
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by samirpandeyit62 » Tue Sep 04, 2007 10:48 pm
Hi Saurav,
I think you have made a typo in the Question, a Probabilty lies between 0 & 1, how can it be greater that 21.
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by samirpandeyit62 » Wed Sep 05, 2007 8:19 am
There are a total of 10 people,
so 2 can be selected out of 10 in 10C2 =45 ways

stmt 1 says that probability nos of women is > 5

lets try with 6 now if there are 6 women then we can select
2 out of 6 in 6C2 ways i.e. 15 ways

so probability that both are women is 15/45 =1/3
this is less than 1/2

howver if u try with 8 women then u would get a probabilty > 1/2

so NOT SUFF

stmt 2 says that probabilty of selecting both men is less than 1/10

let M be the favourable nos of outcomes for selecting both men

then we have M/45 < 1/10
hence M < 4.5
now if nos of men is 2 only then we have 2C2 =1 outcome (valid less than 4.5)
now if we take total nos of men as 3 then 3C2 = 3 ways (valid < 4.5)
if it is 4 then we 4C2 =6 outcomes (no valid here)

hence max nos of men in the group can be 3 here

so nos of women = 7 (min)

hence we can say that 2 women can be selected out of 7 in 7C2 ways =21 ways

hence probability = 21/45 whcih is still less than 1/2

howver if again u try with nos of men =2 and women = 8 then again
u will get a probabilty greater than half

hence NOT sufficeint

If we combine both then also we cannot say any thing as both indirectly
imply the same. HENCE NOT SUFF

so answer should be E

pls see whether this is correct.
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