Question

Instead of using the values {1,2,3,4,5,6) on dice, suppose a pair of dice have the following: {1,2,2,3,3,4} on one die and {1,3,4,5,6,8} on the other. Find the probability of rolling a sum of 6 with these dice. Be sure to reduce.​

Answer 1

the probability of rolling a sum of 6 with these dice is 1/6.

Explanation:

To find the probability of rolling a sum of 6 with the given pair of dice, we can first list all possible pairs of outcomes that add up to 6:

(2,4)

(3,3)

(4,2)

For each of these pairs, we need to find the probability of rolling each number on its respective die and then multiply those probabilities together. The probability of rolling a particular number on one die is the number of times that number appears on that die divided by the total number of outcomes on that die.

For the first pair (2,4), the probability is:

(2 appears twice on one die out of six possible outcomes) × (4 appears once on the other die out of six possible outcomes) = (2/6) × (1/6) = 1/18

For the second pair (3,3), the probability is:

(3 appears twice on one die out of six possible outcomes) × (3 appears twice on the other die out of six possible outcomes) = (2/6) × (2/6) = 4/36

For the third pair (4,2), the probability is:

(4 appears twice on one die out of six possible outcomes) × (2 appears twice on the other die out of six possible outcomes) = (2/6) × (2/6) = 4/36

The total probability of rolling a sum of 6 is the sum of the probabilities of each possible pair:

1/18 + 4/36 + 4/36 = 1/6

Therefore, the probability of rolling a sum of 6 with these dice is 1/6.