Dice probability

Question

A pair of dice is rolled. Find the probabilities of the given events. (Enter exact numbers as integers, fractions, or decimals.)

(a) The sum is 6.

(b) The sum is 6, given that the sum is less than 8.

(c) The sum is less than 8, given that the sum is 6.

Answer 1

Since each dice has 6 faces and we have 2 dice, we have 6², or 36 total possible outcomes. The 36 outcomes can be viewed here: https://study.com/cimages/multimages/16/rolling2dice22666906092574416484.png

(a) The ways we can get a sum of 6 are (1,5), (5,1), (2,3), and (3,2), which is 4 outcomes.

4/36

(b) According to the list of 36 outcomes, only 21 of them have a sum less than 8, therefore 21 is our new denominator. Out of those 21 outcomes, we want to find how many give us a sum of 6. Again, those are (1,5), (5,1), (2,3), and (3,2), which is 4 outcomes.

4/21

(c) According to the list of 36 outcomes, only 4 of them give us a sum of 6, so 4 is our new denominator. Out of those 4 outcomes, we want to find how many give us a sum of 8. That would be none of them.

0/4. (This answer of 0 should be intuitively obvious because if we're given is that the sum if 6, then our sum can not be 8)