The question goes as follows: A pair of dice (with sides numbered 1 through 6) a

Question

The question goes as follows: A pair of dice (with sides numbered 1 through 6) are rolled 10times. For each roll of the dice the sum of the dice is noted.Suppose that the dice are rolled ten times. Find the probabilitythat exactly twice a "2", "7", or "11" is rolled. I am not sure how to approach this question. Please help! Thank you! The question goes as follows: A pair of dice (with sides numbered 1 through 6) are rolled 10times. For each roll of the dice the sum of the dice is noted.Suppose that the dice are rolled ten times. Find the probabilitythat exactly twice a "2", "7", or "11" is rolled. I am not sure how to approach this question. Please help! Thank you!

Explanation / Answer

in such a question you need to understand what are the all possibleways of obtaining a particular output sum of the dice : possible number of ways : probability ofoccurunce obtained by dividing possible ways by total ways 2 : 1 : 1/36 3 : 2 : 2/36 4 : 3 : 3/36 5 : 4 : 4/36 6 : 5 : 5/36 7 : 6 : 6/36 8 : 5 : 5/36 9 : 4 : 4/36 10 : 3 : 3/36 11 : 2 : 2/36 12 : 1 : 1/36 hence total number of ways = 36 now the question wants out of ten times exactly two times 2,7,11 sothe rest that is 4 times we can have any of the following1,3,4,5,6,8,9,10,12 so the total number of having all these is36-2-6-1 = 27 thus number of ways of choosing 2 out of 10 such a choice has to be made thrice once each for 2,7,11 hence 10C2*8C2*6C2*(1/36)^2 * (6/36)^2 * (2/36)^2 * (27/36)^4 =4.9450*10^-5

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