Question

Two dice are rolled. What is the probability that the sum of numbers rolled is either 4 or 12?

Answer 1

Explanation:

Given, Two dice are rolled. We have to find what is the probability that the sum of numbers rolled is either 5 or 12We know that, probability of an event = Now, total outcomes for two dices = 6 for 1st dice x 6 for 2nd dice = 6 x 6 = 36.Now, favourable outcomes = sum is 5 + sum is 12= 4[(1,4), (2,3), (3, 2), (4, 1)] + 1[(6,6)]= 5 total favourable outcomes.Now, probability = 5/36Hence, the probability that sum is either 5 or 12 is 5/36.

Answer 2

the probability of rolling a sum of either 4 or 12 on two dice is 7/36, or approximately 0.1944.

Explanation:

To find the probability of rolling a sum of either 4 or 12 on two dice, we can use the following steps:

Find the total number of possible outcomes when rolling two dice. Each die has 6 possible outcomes, so the total number of outcomes is 6 x 6 = 36.

Find the number of outcomes that result in a sum of 4 or 12.

For a sum of 4, the possible outcomes are (1, 3), (2, 2), and (3, 1). There are two ways to roll each of these outcomes (for example, you can roll a 1 on the first die and a 3 on the second, or you can roll a 3 on the first die and a 1 on the second), so there are 2 x 3 = 6 outcomes that result in a sum of 4.

For a sum of 12, the only possible outcome is (6, 6). There is only one way to roll this outcome, so there is 1 outcome that results in a sum of 12.

Add the number of outcomes that result in a sum of 4 or 12:

6 + 1 = 7

Divide the number of outcomes that result in a sum of 4 or 12 by the total number of possible outcomes:

7/36

Therefore, the probability of rolling a sum of either 4 or 12 on two dice is 7/36, or approximately 0.1944.