We Toss Two Dice 1,000 Times. How Many Times Do We Expect To Have The Sum Of The Two Dice Equal To 4? Please Show Your Steps :)

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There are 36 possible outcomes from rolling 2 dice. Of these, 3 outcomes are a sum of 4. The probability of a sum of 4 on one roll is 3/36 = 1/12. The expected value of the number of 4s in 1000 rolls is (1/12)*1000 = 83 1/3.


There is some probability associated with each number of times the dice will come up 4. For example, the probability that the number of "4" rolls is exactly 83 is about 0.045649. The probability is only slightly more than half that the number of 4s will fall in the range 77 to 89.

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