Question 655222: 5 names need to be drawn from a pool of 10 and they are done so by putting them in a bag and using a blind draw. My question is - are the chances the same whether the blind draw is one name at a time, until 5 have been drawn, or drawing all 5 at once. It doesn't seem like it should matter either way, yet the first way (one at a time) also appears to give the first name a 10% chance, the second one a 11.1% chance (1/9), the third one a 12.5% chance (1/8) and so on until the fifth and final name has a 16.7% chance, which is a bit higher than the first one at only 10%. I'm confused!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 5 names need to be drawn from a pool of 10 and they are done so by putting them in a bag and using a blind draw.
My question is - are the chances the same whether the blind draw is one name at a time, until 5 have been drawn, or drawing all 5 at once.
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5 at a time:
# of possible outcomes: 10C5 = 252 unique groups of 5 names
# of ways to win: 1 group of 5 names
P(choose correct 5 from 10) = 1/10C5 = 1/252 = 0.003968...
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One at a time:
1st good: 5/10
2nd good: 4/9
3rd good: 3/8
4th good: 2/7
5th good: 1/6
P(5 correct names) = (5*4*3*2*1)/(10*9*8*7*6) = 1/10C5 = 0.003969...
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The results are the same.
Cheers,
Stan H.
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