Question

assign probabilities to the outcomes sample space of 3 rolled dice. do probabilities add up to 1.

Answer 1

Let, we through 3 six-sided dice.

Here, each dice has 6 face i.e, 1,2,3,4,5,6 and the probability of getting any one is equally likely or same chance.

So, the total possible outcomes for this experiment is

Here, each of the possible outcome has the probability   being occur in the sample space.

Here, we can consider the possible sum of the dice.

The smallest possible sum(i.e, 3) occurs when all of the dice are smallest and the greatest sum(i.e, 18) occurs when all the dice are greatest.

Here given below the possible sum and total possible way

• There is only 1 way total possible sum is 3.
• There is 3 ways total possible sum is 4
• There is 6 ways total possible sum is 5
• There is 10 ways total possible sum is 6
• There is 15 ways total possible sum is 7
• There is 21 ways total possible sum is 8
• There is 25 ways total possible sum is 9
• There is 27 ways total possible sum is 10
• There is 27 ways total possible sum is 11
• There is 25 ways total possible sum is 12
• There is 21 ways total possible sum is 13
• There is 15 ways total possible sum is 14
• There is 10 ways total possible sum is 15
• There is 6 ways total possible sum is 16
• There is 3 ways total possible sum is 17
• There is 1 way total possible sum is 18