If 3 men and 4 women are being considered for election to the executiv

Question

If 3 men and 4 women are being considered for election to the executive board of a co-op, which has 3 positions, which of the following is the approximate probability that the executive board will not be all men?

A. 0.00
B. 0.03
C. 0.10
D. 0.42
E. 0.97

A. 0.00
B. 0.03
C. 0.10
D. 0.42
E. 0.97

BrentGMATPrepNow · Answer

P(the 3 selections are not ALL male) = 1 -   P(all 3 selections ARE male)  
 
  P(all 3 selections ARE male)   = P(1st person selected is male   AND   2nd person selected is male   AND   3rd person selected is male)
= P(1st person selected is male)   x   P(2nd person selected is male)   AND   P(3rd person selected is male)
= 3/7   x   2/6   x   1/5
= 1/35
≈ 0.029
≈   0.03

So, P(the 3 selections are not ALL male) = 1 -   0.03  
= 0.97

Answer: E

mohshu · Answer

GMATPrepNow  @brent the question asks for the probability that all will not be men..
ans shud be E..

please let me know if im going wrong anywhere..
thanks

broall · Answer

IMO, the selection doesn't care about the order, so there are $3C3=1$ ways to select all men to the executive board of a co-op.

There are $7C3$ ways to select 3 people to the executive board of a co-op.

Hence, there are $7C3-1$ ways to select 3 people, at least one of them are women.

The approximate probability that the executive board will not be all men:
$\frac{7C3-1}{7C3}=\frac{34}{35} \approx 0.97$

The answer is E.

BrentGMATPrepNow · Answer

Good catch - I completed missed the word "not"

I've edited my response accordingly. Cheers and thanks, Brent

Nunuboy1994 · Answer

We can essentially translate this question as- what is the probability that at least one woman will be chosen- because if one woman is chosen then that constitutes an executive board that is NOT entirely male. Apply the rule of complementary probability, or rather negate this event...1 minus the probability of ALL men being chosen.

1- 3c3/7c3 = 34/35

0.97

E.

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If 3 men and 4 women are being considered for election to the executiv

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If 3 men and 4 women are being considered for election to the executiv

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