3 times (out of 36) is the probablility
Possible Outcome 1 - Dice 1: 4, Dice 2: 6
Possible Outcome 2 - Dice 1: 5, Dice 2: 5
Possible Outcome 3 - Dice 1: 6, Dice 2: 4
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The probability of rolling a 4 in a die is 1 in 6, or about 0.1667. The probability, then, of rolling a 4 in at least one of two dice rolls is twice that, or 2 in 6, or 0.3333. The probability of rolling a sum of 4 in two dice is 3 in 36, or 1 in 18, or about 0.05556.
The probability of rolling a sum of 8 on one roll of a pair of dice is 5/36.The probability of not rolling a sum of 8 on one roll of a pair of dice is 31/36.The probability of rolling a sum of 8 twice on two rolls of a pair of dice is(5/36)(5/36) = (5/36)2 .The probability of rolling first a sum of 8 and then rolling a sum that is not 8 on thesecond roll is (5/36)(31/36).The probability of rolling a sum that is not 8 on the first roll and rolling a sum of 8in the second roll is (31/36)(5/36).So The probability of rolling a sum of 8 at least one of two rolls of a pair of dice is(5/36)2 + (5/36)(31/38) + (31/36)(5/36) = 0.258487654... ≈ 25.8%.
The probability of rolling a sum of 8 with two dice is 5 in 36 or about 0.1389. 2 and 6 3 and 5 4 and 4 5 and 3 6 and 2
There are 36 permutations of two dice. Of these, 9 have a sum of 5 or 6, so the probability of rolling a sum of 5 or 6 on two dice is 9 in 36, or 1 in 9, or about 0.1111.
Prob(Sum is not divisible by 3) = 24/36 = 2/3