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If two fair six-sided dice are thrown, what is the probability that th

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Carcass
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If two fair six-sided dice are thrown, what is the probability that th [#permalink] New post   27 Sep 2021, 05:14
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If two fair six-sided dice are thrown, what is the probability that the sum of the numbers showing on the dice is 6 ?

(A) 1/36
(B) 1/12
(C) 5/36
(D) 1/6
(E) 1
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C
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eskay1981
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Re: If two fair six-sided dice are thrown, what is the probability that th [#permalink] New post   27 Sep 2021, 10:07
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Carcass wrote:
If two fair six-sided dice are thrown, what is the probability that the sum of the numbers showing on the dice is 6 ?

(A) 1/36
(B) 1/12
(C) 5/36
(D) 1/6
(E) 1


For two 6-sided dice, the number of ways the sum to be 6 are {(1,5),(2,4),(3,3),(4,2),(5,1)}
So 5/36.
Answer is C) 5/36
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Re: If two fair six-sided dice are thrown, what is the probability that th [#permalink] New post   12 Oct 2021, 01:51
why we do not count (3, 3) twice? so that the p = 6/36
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Re: If two fair six-sided dice are thrown, what is the probability that th [#permalink] New post   12 Oct 2021, 19:56
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It is necessary to consider each case one time only.
Both values are the same, so there will be an error in the counting. (3,3) is the same on either side hence considered once only.

vaughan88 wrote:
why we do not count (3, 3) twice? so that the p = 6/36
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Re: If two fair six-sided dice are thrown, what is the probability that th [#permalink] New post   14 Oct 2021, 03:25
vaughan88 wrote:
why we do not count (3, 3) twice? so that the p = 6/36


Vaughan,

Throwing 2 dice can be simplified as throwing the same dice twice. In that case, the (3,3) can't be differentiated and counted twice.
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Re: If two fair six-sided dice are thrown, what is the probability that th [#permalink] New post   15 Oct 2022, 09:53
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Given that two six-sided dice are thrown and we need to find what is the probability that the sum of the numbers shown on the dice is six?

As we are rolling two dice => Number of cases = \(6^2\) = 36

Lets start writing the possible cases where sum of the two rolls = 6. Following are the possible cases:
(1,5)
(2,4)
(3,3)
(4,2)
(5,1)

=> 5 cases

=> Probability that sum of two rolls is 6 = \(\frac{5}{36}\)

So, Answer will be C
Hope it helps!

Watch the following video to learn How to Solve Dice Rolling Probability Problems

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Re: If two fair six-sided dice are thrown, what is the probability that th [#permalink]
15 Oct 2022, 09:53
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