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Michel is drawing 2 winning tickets from a bucket of raffle

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Michel is drawing 2 winning tickets from a bucket of raffle  [#permalink]

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New post 13 Jun 2013, 08:10
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Michel is drawing 2 winning tickets from a bucket of raffle tickets she sold. She sold atleast 14 but not more than 22 tickets. If James bought two tickets from Michel and tickets are not returned to the drawing bucket after they have been drawn what is the lowest possible probability that he will win both prizes?

The OA is not given.


Can somebody please help me with this one. It will be very helpful if you explain every step.
Thanks.
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Re: Michel is drawing 2 winning tickets from a bucket of raffle  [#permalink]

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New post Updated on: 16 Jun 2013, 08:40
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emon wrote:
Michel is drawing 2 winning tickets from a bucket of raffle tickets she sold. She sold atleast 14 but not more than 22 tickets. If James bought two tickets from Michel and tickets are not returned to the drawing bucket after they have been drawn what is the lowest possible probability that he will win both prizes?

The OA is not given.


Can somebody please help me with this one. It will be very helpful if you explain every step.
Thanks.


Hi Emon, I'll try and walk you through this. Please let me know if anything is unclear or if I maybe misunderstood something.

If James has the two winning tickets, and the question is asking the lowest possible probability that he won both prizes, then we need to maximize the number of tickets sold (i.e. 22). If they only sold 2 tickets, he'd be a guaranteed winner, so the more tickets sold, the less chance he has to be the winner.

Now that we know there are 22 tickets sold, and James has 2, what are the chances that the first one will be a winner? His number of tickets over the total number of tickets, so 2/22. We only care about the scenario where he wins, so let's assume he wins the first drawing. For the second drawing, he now has 1 chance out of 21 remaining tickets to win, so 1/21. Multiplying these two together (and simplifying by 2) we get 1/11 * 1/21 = 1/231. He has about a half a percentage chance to win both drawings if she sold 22 tickets.

Again, if she'd sold 20, 18 or 14 tickets, James' odds of winning would go up, so the lowest percentage possible should be 1/231, i.e. the odds that he wins the first x the odds that he wins the second.

Hope this helps!
-Ron
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Originally posted by VeritasPrepRon on 13 Jun 2013, 09:12.
Last edited by VeritasPrepRon on 16 Jun 2013, 08:40, edited 1 time in total.
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Re: Michel is drawing 2 winning tickets from a bucket of raffle  [#permalink]

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New post 16 Jun 2013, 05:08
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VeritasPrepRon wrote:
emon wrote:
Michel is drawing 2 winning tickets from a bucket of raffle tickets she sold. She sold atleast 14 but not more than 22 tickets. If James bought two tickets from Michel and tickets are not returned to the drawing bucket after they have been drawn what is the lowest possible probability that he will win both prizes?

The OA is not given.


Can somebody please help me with this one. It will be very helpful if you explain every step.
Thanks.


Hi Emon, I'll try and walk you through this. Please let me know if anything is unclear or if I maybe misunderstood something.

If James has the two winning tickets, and the question is asking the lowest possible probability that he won both prizes, then we need to maximize the number of tickets sold (i.e. 22). If they only sold 2 tickets, he'd be a guaranteed winner, so the more tickets sold, the less chance he has to be the winner.

Now that we know there are 22 tickets sold, and James has 2, what are the chances that the first one will be a winner? His number of tickets over the total number of tickets, so 2/22. We only care about the scenario where he wins, so let's assume he wins the first drawing. For the second drawing, he now has 1 chance out of 21 remaining tickets to win, so 1/21. Multiplying these two together (and simplifying by 2) we get 1/11 * 1/21 = 1/232. He has about a half a percentage chance to win both drawings if she sold 22 tickets.

Again, if she'd sold 20, 18 or 14 tickets, James' odds of winning would go up, so the lowest percentage possible should be 1/232, i.e. the odds that he wins the first x the odds that he wins the second.

Hope this helps!
-Ron


Should have been 1/231 :)
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Re: Michel is drawing 2 winning tickets from a bucket of raffle  [#permalink]

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New post 16 Jun 2013, 08:39
Yes absolutely! Multiplying two simple numbers is trixy!!

That's why I always prefer to have answer choices. I'll edit my post. Thanks!

-Ron
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Re: Michel is drawing 2 winning tickets from a bucket of raffle  [#permalink]

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New post 16 Jun 2013, 09:15
The chance for James to win prize in the first ticket is 1/22, the chance to win in the second is 1/21. So the lowest possibility is 1/21x22, not 1/11x21. Could please you help me explain this, Ron?
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Re: Michel is drawing 2 winning tickets from a bucket of raffle  [#permalink]

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New post 16 Jun 2013, 09:54
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kloklo wrote:
The chance for James to win prize in the first ticket is 1/22, the chance to win in the second is 1/21. So the lowest possibility is 1/21x22, not 1/11x21. Could please you help me explain this, Ron?


Sure thing kloklo, the issue is that James has 2 tickets, so his chances of winning the first prize is 2/22, not 1/22. I simplify the expression to make the math easier, but his chances are basically the number of tickets he has / number of tickets issued. If he'd had 21 tickets out of 22, his chances of winning would be very high indeed!

Hope this helps!
-Ron
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Re: Michel is drawing 2 winning tickets from a bucket of raffle   [#permalink] 16 Jun 2013, 09:54
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