Question

When two dice are rolled, 36 equally likely outcomes are possible as shown below. (1, 1) (1, 2) ... Which chart shows the probability distribution for the sum of the two numbers?

Option 1: Chart A
Option 2: Chart B
Option 3: Chart C
Option 4: None of the above

Answer 1

When two dice are rolled, there are 36 equally likely outcomes. To create a probability distribution for the sum of the two numbers, count the number of outcomes for each possible sum and divide it by 36.

Step-by-step explanation:

When two dice are rolled, there are 36 equally likely outcomes. Each outcome is represented by a pair of numbers, where the first number represents the result of the first roll and the second number represents the result of the second roll. To create a probability distribution for the sum of the two numbers, we count the number of outcomes for each possible sum and divide it by the total number of outcomes (36).

For example, the sum of 2 can only occur if both dice show a 1, so the probability of getting a sum of 2 is 1/36. The sum of 3 can be obtained in two ways (1, 2) or (2, 1), so the probability is 2/36. Similarly, the sum of 4 can be obtained in three ways (1, 3), (2, 2), or (3, 1), so the probability is 3/36.

By counting all the possible outcomes for each sum and calculating the corresponding probability, we can create a probability distribution for the sum of the two numbers rolled.