Eight women and two men are available to serve on a committee. If thre

Question

Eight women and two men are available to serve on a committee. If three people are picked, what is the probability that the committee includes at least one man?

(A)  \frac{1}{32}

(B)  \frac{1}{4}

(C)  \frac{2}{5}

(D)  \frac{7}{15}

(E)  \frac{8}{15}

LevanKhukhunashvili · Accepted Answer

We have to apply 1-p approach

What is the probability that the committee doesn't include man?
 \frac{8}{10} * \frac{7}{9} * \frac{6}{8} = \frac{7}{15}

What is the probability that the committee includes at least one man? 1- \frac{7}{15} = \frac{8}{15}

IMO
Ans:  E

sudarshan22 · Answer

2 men 1 women = 2C2 * 8C1 = 8
1 men 2 women = 2C1 * 8C2 = 56
Combing both 8 + 56 = 64
Total = 10C3 = 120

Required probabiity = 64 / 120 = 8/15

Hence,   E  .

BrentGMATPrepNow · Answer

When it comes to probability questions involving "at least," it's best to try using the  complement . 
That is, P(Event A happening) = 1 - P(Event A  not  happening)
So, here we get: P(getting at least 1 man) = 1 -  P( not  getting at least 1 man) 
What does it mean to  not  get at least 1 man? It means getting ZERO men. 
So, we can write: P(getting at least 1 man) = 1 -  P(getting ZERO men)

P(getting ZERO men)  
P(getting ZERO men) = P(all 3 selections are women)
= P(1st selection is a woman   AND   2nd selection is a woman   AND   3rd selection is a woman)
= P(1st selection is a woman)   x   P(2nd selection is a woman)   x   P(3rd selection is a woman)
= 8/10   x   7/9   x   6/8
=  7/15

So we get: P(getting at least 1 man) = 1 -  7/15 
= 8/15

Answer: E

Cheers,
Brent

KarishmaB · Answer

Let's find how many committees we can make with no men. We can subtract that out of the total number of committees to get how many committees will have at least 1 man.

8 women and 2 men

Select a committee with all women = 8C3 = 8*7*6/3*2 = 56

Select a committee in all possible ways = 10C3 = 10*9*8/3*2 = 120

No of committees with at least 1 man = 120 - 56 = 64

Req Probability = 64/120 = 8/15

Answer (E)

ScottTargetTestPrep · Answer

P(at least one man) = 1 - P(no men) = 1 - P(all women)

P(all women) = 8/10 x 7/9 x 6/8 = 4/5 x 7/9 x 3/4 = 3/5 x 7/9 = 21/45 = 7/15

P(at least one man) = 1 - 7/15 = 8/15

Answer: E

Paras96 · Answer

Eight women and two men are available to serve on a committee. If three people are picked, what is the probability that the committee includes at least one man?

Probability(committee includes at least one man) = 1 - Probability(committee includes no man) = 1 - 8C3/10C3 = 1 - 7/15 = 8/15

Hence E

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Eight women and two men are available to serve on a committee. If thre

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