Question

four fair 6-sided dice are rolled. the sum of the numbers shown on the dice is 8. what is the probability that 2's were rolled on all four dice?

Answer 1

The probability of rolling 2's on all four dice when the sum is 8 is 1/1296.The likelihood of obtaining a sum of 8 by rolling four 2's on four dice is 1 in 1296.

Step-by-step explanation:

To find the probability of rolling 2's on all four dice when the sum is 8, we need to determine the number of ways this can occur and divide it by the total number of possible outcomes.

There is only one way to get a sum of 8 with four dice, which is rolling four 2's. The total number of possible outcomes when rolling four six-sided dice is 6^4 (since each die has 6 possible outcomes).

Therefore, the probability of rolling 2's on all four dice is 1/6^4, or 1/1296.

To ascertain the probability of rolling four 2's on four six-sided dice and achieving a sum of 8, we recognize there's only one favorable outcome. Dividing this by the total possibilities (6^4), we obtain the probability: 1/6^4 or 1/1296. This calculation provides a precise understanding of the likelihood of rolling the specific combination desired amid all potential outcomes with the four dice.