1.   A committee of 5 is to be formed from a group of 6 men and 5 women. if this individuals have an equal chance of being selected, what is the probability that the numbers are:

 

a.   all men

b.   two are men and three are women

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1 Answer

a. There are 11 people, so the chance of picking a man first is 6/11, leaving 5 men and 5 women. If the second is also a man, the chances of picking one are 1/2; for the third man it's 4/9, then 3/8 and 2/7. The combined probability is 6/11*1/2*4/9*3/8*2/7=1.3% approx.

b. Let's assume that the order is 2 men then 3 women (we address the problem of other orders later). For the two men the combined probability is 6/11*1/2=3/11. There are 4 men and 5 women left, so the combined probabilities for the women are 5/9*1/2*3/7=15/126=5/42=11.9% approx. But we have to consider how many ways 2 men and 3 women can be selected:

MMWWW, MWMWW, MWWMW, MWWWM, WMMWW, WMWMW, WMWWM, WWMMW, WWMWM, WWWMM.

Therefore we need to multiply the combined probabilities by 10: 3/11*5/42*10=32.47% approx.

 

by Top Rated User (1.2m points)

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