A club consists of 36 men and 24 women. If 5 people are selected at random for a party committee, what is the probability that the committee will be all women?
2007-11-11 12:33:50 · 5 answers · asked by lilred 1 in Science & Mathematics ➔ Mathematics
There are 60 people in total.
So the probability of picking a woman the first time is 24/60. The probability of picking a woman the second time is 23/60, and so on. So you would do...
24 x 23 x 22 x 21 x 20= 5100480
60^5 = 777600000
So the answer is 5100480 / 777600000.
But you can reduce that.
So the answer is 1771/270000
Which is = .778%
2007-11-11 12:48:05 · answer #1 · answered by Lt Weasel1225 3 · 0⤊ 1⤋
Probability is simply a ratio of favorable outcome to total outcomes. In this case, you have a total of 60 people in the club. Since you have 24 women in the club, the probability that the first selection is female would be 24/60, which reduced is 2/5. After the first selection is taken, you have 23 women and 59 total people left. Therefore, the probability the next person selected is female is 23/59, which doesn't reduce. The next is 22/58, or 16/29.
You simply multiply the first five probabilities together to get the probability that all five chosen will be female.
2/5 x 23/59 x 16/29 x 7/19 x 5/14 = 368/32,509 or approximately 1.13%
2007-11-11 20:50:18 · answer #2 · answered by Anonymous · 0⤊ 1⤋
(24 choose 5)/(60 choose 5) = 42504/5461512 â 0.00778
2007-11-11 20:45:09 · answer #3 · answered by Ron W 7 · 0⤊ 0⤋
P(all 5 women)
= 24C5 / (36+24)C5
= 24C5 / 60C5
= 42504 / 5461512
= 0.778%
2007-11-11 20:45:18 · answer #4 · answered by Mugen is Strong 7 · 0⤊ 0⤋
(24/36)^5
2007-11-11 20:52:42 · answer #5 · answered by ivblackward 5 · 0⤊ 1⤋