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# When two dice are thrown, what is the probability that the score on th

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Intern
Joined: 01 Jun 2010
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When two dice are thrown, what is the probability that the score on th [#permalink]

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07 Jun 2010, 06:57
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86% (00:47) correct 14% (01:12) wrong based on 8 sessions

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When two dice are thrown, what is the probability that the score on the second dice is higher than the score on the first dice?

[Reveal] Spoiler:
5/12
Intern
Joined: 01 Jun 2010
Posts: 4
Re: When two dice are thrown, what is the probability that the score on th [#permalink]

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07 Jun 2010, 07:03
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I understand now

1) First dice: 1 ... Second dice: 2, 3, 4, 5, or 6 ... P=(1/6)*(5/6)
2) First dice: 2 ... Second dice: 3, 4, 5, or 6 ... P=(1/6)*(4/6)
3) First dice: 3 ... Second dice: 4, 5, or 6 ... P=(1/6)*(3/6)
4) First dice: 4 ... Second dice: 5 or 6 ... P=(1/6)*(2/6)
5) First dice: 5 ... Second dice: 6 ... P=(1/6)*(1/6)

The sum of probabilities of the 5 scenarios: 15/36
Math Expert
Joined: 02 Sep 2009
Posts: 43892
Re: When two dice are thrown, what is the probability that the score on th [#permalink]

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07 Jun 2010, 07:33
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test800 wrote:
When two dice are thrown, what is the probability that the score on the second dice is higher than the score on the first dice?

[Reveal] Spoiler:
5/12

There are 6*6=36 possible outcomes when you throw 2 dice.

In 6 of these outcomes there will be a tie (1-1, 2-2, 3-3, ..., 6-6). 30 outcomes left: now in half of these outcomes (30/2=15) the score of die #1 will be more than the score of die #2 and in another half of the outcomes the score of die #1 will be less than the score of die #2. So $$P(#2>#1)=\frac{15}{36}=\frac{5}{12}$$.

Answer: $$\frac{5}{12}$$.

Hope it helps.
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Re: When two dice are thrown, what is the probability that the score on th [#permalink]

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19 Oct 2017, 20:34
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: When two dice are thrown, what is the probability that the score on th   [#permalink] 19 Oct 2017, 20:34
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