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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 both prizes?

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


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Bunuel
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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 both prizes?

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, 04:57
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The probability to win both prizes

Two winning tickets out of 3 can be chosen in \(^3{C_2}\) ways = 3

Two tickets out of 200 can b given in \(^{200}{C_2}\) ways = 19900

P = 3/19900

We don't have this option....
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In a raffle in which 200 tickets are sold, there are 3 prizes - first [#permalink] New post   Updated on: 02 Dec 2020, 07:17
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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 both prizes?

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


Hi Bunuel,
I think you're missing an answer choice :)

Imagine that there are 200 balls in a box, 3 of which are "winning" balls.
The man will randomly draw two balls without replacement.

So, P(select 2 winning balls) = P(1st ball is winner AND 2nd ball is winner)
= P(1st ball is winner) x P(2nd ball is winner)
= 3/200 x 2/199
= 3/19,900

Answer: A

Originally posted by BrentGMATPrepNow on 02 Dec 2020, 06:58.
Last edited by BrentGMATPrepNow on 02 Dec 2020, 07:17, edited 1 time in total.
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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, 07:11
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BrentGMATPrepNow wrote:
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 both prizes?

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


Imagine that there are 200 balls in a box, 3 of which are "winning" balls.
The man will randomly draw two balls without replacement.

So, P(select 2 winning balls) = P(1st ball is winner AND 2nd ball is winner)
= P(1st ball is winner) x P(2nd ball is winner)
= 3/200 x 2/199
= 3/19,900

Hi Bunuel,
I think you're missing an answer choice :)

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Edited the typo. Thank you!
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Re: In a raffle in which 200 tickets are sold, there are 3 prizes - first [#permalink]
02 Dec 2020, 07:11
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