SOLUTION: Mary buys 2 tickets for a raffle where 2 prizes are awarded. If 50 tickets are sold, the probability that Mary wins at least 1 prize is
A.
97/1225
B.
1/1225
C.
1128/122
Algebra ->
Probability-and-statistics
-> SOLUTION: Mary buys 2 tickets for a raffle where 2 prizes are awarded. If 50 tickets are sold, the probability that Mary wins at least 1 prize is
A.
97/1225
B.
1/1225
C.
1128/122
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Question 1098791: Mary buys 2 tickets for a raffle where 2 prizes are awarded. If 50 tickets are sold, the probability that Mary wins at least 1 prize is
A.
97/1225
B.
1/1225
C.
1128/1225
D.
1/2450 Found 2 solutions by richwmiller, greenestamps:Answer by richwmiller(17219) (Show Source):
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You can put this solution on YOUR website! Winning at least one prize is the "opposite" of not winning either one. So the probability of winning at least one prize is 1 minus the probability of not winning either prize.
When the first winning ticket number is drawn, the probability that Mary does not win is 48/50.
When the second winning number is drawn, the probability that she does not win is 47/49.
The probability that she doesn't win either prize is
So the probability that she wins at least one prize is
...OR...
You can get this answer by finding the probability that
EITHER she wins when the first prize is drawn,
OR she doesn't win when the first prize is drawn but wins when the second prize is drawn.
The probability that she wins when the first card is drawn is 2/50 = 1/25.
The probability that she DOESN'T win on the first draw is 48/50; then the probability that she DOES win on the second draw is 2/49. So the probability that she doesn't win on the first draw and wins on the second is .
Then the probability that she wins on at least one of the draws is
Especially when you are first learning how to find probabilities, it is a good exercise to be able to solve a problem by two different methods and see that you get the same answer....
