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In a raffle in which 200 tickets are sold, there are 3 prizes - first

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Bunuel
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In a raffle in which 200 tickets are sold, there are 3 prizes - first [#permalink] New post   02 Dec 2020, 04:45
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In a raffle in which 200 tickets are sold, there are 3 prizes - first prize of $100, second prize of $50, third prize of $30. A man has 2 tickets in this raffle. WHat is the probability that he wins a prize ?

A. 1/19900
B. 1/100
C. 3/200
D. 297/9950
E. 1/10


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Re: In a raffle in which 200 tickets are sold, there are 3 prizes - first [#permalink] New post   02 Dec 2020, 06:30
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Bunuel wrote:
In a raffle in which 200 tickets are sold, there are 3 prizes - first prize of $100, second prize of $50, third prize of $30. A man has 2 tickets in this raffle. WHat is the probability that he wins a prize ?

A. 1/19900
B. 1/100
C. 3/200
D. 297/9950
E. 1/10




We have 200 raffle tickets, of which we have 3 winning numbers.

The man has 2 raffle tickets.

Probability = Favorable Outcomes / Total Outcomes

Total Outcomes = 200C2 = 100 * 199 (Since we are going to choose 2 of the numbers with 2 raffle tickets)

Favorable Outcomes = Winning a prize = Winning with 1 ticket and not winning with the other + Winning with both Tickets

There are 3 winning numbers and 200 - 3 = 197 non winning numbers

Winning with 1 ticket and not winning with the other = 3C1 + 197C1 = 3 * 197 = 591

Winning with both Tickets = 3C2 = 3

Total Favorable Outcomes = 591 + 3 = 594


Probability = Favorable Outcomes / Total Outcomes = 594 / (100 * 199) = 297 / 9950


Option D

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Re: In a raffle in which 200 tickets are sold, there are 3 prizes - first [#permalink] New post   02 Dec 2020, 04:47
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Bunuel wrote:
In a raffle in which 200 tickets are sold, there are 3 prizes - first prize of $100, second prize of $50, third prize of $30. A man has 2 tickets in this raffle. WHat is the probability that he wins a prize ?

A. 1/19900
B. 1/100
C. 3/200
D. 297/9950
E. 1/10


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Re: In a raffle in which 200 tickets are sold, there are 3 prizes - first [#permalink] New post   26 Aug 2022, 22:36
@banuel - Any simpler solution to this please?
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Re: In a raffle in which 200 tickets are sold, there are 3 prizes - first [#permalink] New post   27 Aug 2022, 04:58
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The probability of winning a prize = 1 - the probability of not winning the prize. In order to not win the prize, both the first and the second drawn tickets have to be non-winning tickets. Since there are 3 winning tickets, the probability of drawing the first non-winning ticket is 197/200. Similarly, the probability that the second ticket will be non-winning given that we have drawn the first non-winning ticket is 196/199.

So the answer to our question is P = 1 - 197/200 * 196/199, which after simplification becomes 297/9950
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Re: In a raffle in which 200 tickets are sold, there are 3 prizes - first [#permalink] New post   27 Aug 2022, 05:03
Raidas wrote:
The probability of winning a prize = 1 - the probability of not winning the prize. In order to not win the prize, both the first and the second drawn tickets have to be non-winning tickets. Since there are 3 winning tickets, the probability of drawing the first non-winning ticket is 197/200. Similarly, the probability that the second ticket will be non-winning given that we have drawn the first non-winning ticket is 196/199.

So the answer to our question is P = 1 - 197/200 * 196/199, which after simplification becomes 297/9950



Very clear. Thanks

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Re: In a raffle in which 200 tickets are sold, there are 3 prizes - first [#permalink] New post   11 Feb 2024, 06:09
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Re: In a raffle in which 200 tickets are sold, there are 3 prizes - first [#permalink]
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