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Probability hard question by MIT professor walter Lewin

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alimuhammadtariq
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Probability hard question by MIT professor walter Lewin [#permalink] New post   07 Jun 2017, 05:53
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There are 1000 lotteries
each lottery has 1000 tickets
each lottery has 1 prize
You buy 1 ticket in each of 1000 lotteries thus u end up with 1000 tickets

Q what is the probability that you win at least 3 prizes.



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Re: Probability hard question by MIT professor walter Lewin [#permalink] New post   07 Jun 2017, 05:56
question is on youtube by name "Second (more difficult) Lottery Problem" could not post link as i am new not allowed.
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Re: Probability hard question by MIT professor walter Lewin [#permalink] New post   07 Jun 2017, 06:04
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alimuhammadtariq wrote:
There are 1000 lotteries
each lottery has 1000 tickets
each lottery has 1 prize
You buy 1 ticket in each of 1000 lotteries thus u end up with 1000 tickets

Q what is the probability that you win at least 3 prizes.


would be better if you provide choices..

otherwise this can be solved by finding chances of winning none, 1 or 2 prizes and then subtract from ONE..
winning NONE = \(\frac{999}{1000}^1000\)
winning 1= 1/1000 * (999/1000)^999 * 1000C1
and so on...
now ans = 1- \(\frac{999}{1000}^1000\)-1/1000 * (999/1000)^999 * 1000C1-1/1000 * 1/1000 * (999/1000)^998 * 1000C2
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Re: Probability hard question by MIT professor walter Lewin [#permalink] New post   07 Jun 2017, 06:26
alimuhammadtariq wrote:
There are 1000 lotteries
each lottery has 1000 tickets
each lottery has 1 prize
You buy 1 ticket in each of 1000 lotteries thus u end up with 1000 tickets

Q what is the probability that you win at least 3 prizes.


Probability of winning a lottery = 1/1000
probability of not winning a lottery = 999/1000

probability of winning none = (999/1000)^1000
Probability of winning 1 lottery = 1000 C1 *(999/1000)^999 * 1/1000=(999/1000)^999
Probability of winning 2 lotteries = 1000 C2 * (999/1000)^998 * 1/1000^2 = (999/1000)^999/2

So probability of winning at least 3 prizes = 1- (999/1000)^1000 - (999/1000)^999- (999/1000)^999/2
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Re: Probability hard question by MIT professor walter Lewin [#permalink] New post   07 Jun 2017, 06:27
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alimuhammadtariq wrote:
question is on youtube by name "Second (more difficult) Lottery Problem" could not post link as i am new not allowed.


Kindly post the part of the link leaving https , youtube etc..

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Re: Probability hard question by MIT professor walter Lewin [#permalink] New post   10 Aug 2018, 23:09
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Re: Probability hard question by MIT professor walter Lewin [#permalink]
10 Aug 2018, 23:09
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