SOLUTION: 100 green tickets and 10 red tickets are sold in a raffle in which there are three prizes.. one ticket is drawn for first prizes, discarded, and then a second ticket is drawn for s

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Question 760475: 100 green tickets and 10 red tickets are sold in a raffle in which there are three prizes.. one ticket is drawn for first prizes, discarded, and then a second ticket is drawn for second prize. this is also discarded before the third prize is drawn.
a) what is the probability that all three prizes are won by green tickets?
b) what is the probability that at least one green tickets wins a prize?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
probability of drawing a green ticket on the first draw is 100/110.
probability of drawing a green ticket on second draw assuming you drew a green ticket on the first draw is 99/109.
probability of drawing a green ticket on third draw assuming you drew a green ticket on the first and second draw is 98/108.

the combined probability of getting a green ticket on all 3 draws is equal to 100/110 * 99/109 * 98/108.

pobability of drawing at least 1 green ticket on all 3 draws is equal to 1 minus the probability of drawing 0 green tickets on all 3 draws.

the probability of getting 0 green ticket on all 3 draws is the same as the probability of getting a red ticket on all 3 draws.

p(red) on dirst draw is 10/110.
p(red) on second draw assuming you got a red ticket on first draw is 9/109.
p(red) on third draw is assuming you got a red ticket on first and second draw is 8/108.

combined probability of getting a red ticket on all 3 draws is equal to 10/110 * 9/109 * 8/108.

combined probability of getting 0 green ticket on all 3 draws is the same probability as the probability of getting a red ticket on all 3 draws.

probability of getting at least 1 green ticket on all 3 draws is equal to 1 minus the probability of getting 0 green tickets on all 3 draws which is equal to 1 minus (10/110 * 9/109 * 8/108).