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# Given two fair dice, what is the probability that the sum of their num

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Re: Given two fair dice, what is the probability that the sum of their num [#permalink]
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Aasthabhardwaj5 wrote:
Given that exactly 1 of the dice shows 3, the other dice can have 1,2,4,5,6 as possible results, the probability that sum is 4 would then be probability of getting 1 out of the 5 possible events= 1/5

or it could be the probability of getting 3 on first dice and 1 on second dice = 1/6*1/5 or 1 on first dice, 3 on second dice 1/5*1/6 which would be 1/15 but since getting 3 is given I opted for answer E

I would agree to answer E.

EXACTLY is the catch word.
If exactly one is 3, the other has to be 1. So (1,3) and (3,1) are 2 ways.

However, total ways are
First dice 3, the other can be remaining 5.
First anything other than 3 and second dice 5.
So total 10 ways.

P= 2/10=1/5

If the question said AT LEAST one is 3, then the answer would be the given OA 2/11 as both dice showing 3 will also add up.
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Re: Given two fair dice, what is the probability that the sum of their num [#permalink]
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chetan2u wrote:
Aasthabhardwaj5 wrote:
Given that exactly 1 of the dice shows 3, the other dice can have 1,2,4,5,6 as possible results, the probability that sum is 4 would then be probability of getting 1 out of the 5 possible events= 1/5

or it could be the probability of getting 3 on first dice and 1 on second dice = 1/6*1/5 or 1 on first dice, 3 on second dice 1/5*1/6 which would be 1/15 but since getting 3 is given I opted for answer E

I would agree to answer E.

EXACTLY is the catch word.
If exactly one is 3, the other has to be 1. So (1,3) and (3,1) are 2 ways.

However, total ways are
First dice 3, the other can be remaining 5.
First anything other than 3 and second dice 5.
So total 10 ways.

P= 2/10=1/5

If the question said AT LEAST one is 3, then the answer would be the given OA 2/11 as both dice showing 3 will also add up.

You are given that one die shows a 3. It means the other die does not show a 3. So total cases would be those in which exactly one die shows a 3.
Assuming the dice to be distinct (say Red and Yellow), we can get a sum of 4 in 2 ways (3 on Red, 1 on Yellow or 3 on Yellow and 1 on Red).
The total possible ways with a 3 on exactly one die are 5 (3 on Red and 1/2/4/5/6 on Yellow) + 5 (3 on Yellow and 1/2/4/5/6 on Red) = 10

Probability = 1/5
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Re: Given two fair dice, what is the probability that the sum of their num [#permalink]
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Re: Given two fair dice, what is the probability that the sum of their num [#permalink]
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