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# Two dice each number from 1 to 6 are tossed n times

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GMAT Club Legend
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Two dice each number from 1 to 6 are tossed n times [#permalink]  14 Feb 2004, 23:15
Two dice each number from 1 to 6 are tossed n times
determine the least value of n for which the probability of obtaining at least one double "4" is greater than 1/2
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Best Regards,

Paul

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Joined: 03 Jul 2003
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Computing probability for one dice is itself very complicated.
Two dice ! Hope we won't see these problems in real GMAT

I've used calculator to compute the answers and it is 24.

Method will fallow, if it is correct.
SVP
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If you throw pair of dice once P of not getting double 4 is 5^2/6^2
So if you throw N times then not getting even one double 4 = 5^2n/6^2n
So P of getting atleast one double 4 = (6^2n-5^2n)/6^2n
If we equate it to 1/2
we get
6^2n = 5^2n Only for N = 0 this equation is satisfied.

N cannot be determined.

I may be wrong here.
GMAT Club Legend
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This is how I approached it.
Probability of getting two 4s: 1/6*1/6 = 1/36
When n>18, then probability of getting two 4s will be greater than 1/2. Therefore, 19/36>1/2 and n would then be equal to 19... Btw, there is no OA on this one so it's open to debate
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Paul

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This is the link to the question: http://www.testmagic.com/forum/topic.asp?TOPIC_ID=8960. You got it right kpadma!
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Paul

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Hi folks

I still standby my answer. I went through the link Paul posted.

Paul u r explaination is not correct because as per your explaination
if the experiment is repeated let us say 72 times then P of getting double 4 will be 72/36 = 2

Basically 1-5^2n/6^2n > 1/2
or 5^2n/6^2n < 1/2
so n = 2 this condition is satisfied.
Director
Joined: 03 Jul 2003
Posts: 654
Followers: 2

Kudos [?]: 32 [0], given: 0

Computing probability for one dice is itself very complicated.
Two dice ! Hope we won't see these problems in real GMAT

I've used calculator to compute the answers and it is 24.

Method will fallow, if it is correct.

The probabilty of getting this question in GMAT is less than the probabilty of a nuclear war in a year. (Two years back, Warren E Buffett predicted that the world will see a nuclear war or catastrophe in 20 years)
So, We may have other issues to worry about
campared to this problem.

Ans:

1 - (35/36)^n > 1/2

N = 25.

Qus: Does anyone know a method to solve the above equation
with out a calculator.
SVP
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I realize my mistake. I agree with kpadma.

P of not getting double 4 in a single toss is 1-1/36 = 35/36
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Padma, maybe u could take logs on both sides of the eqn and solve it(with slight approximation).....of course I still did not remember log7........but thats the easiestway!!
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