Question

When two dice are rolled, 36 equally likely outcomes are possible as shown below. (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6) (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6) (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6) (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6) (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) let x be the sum of the two numbers. let p be the probability of the desired outcome. compare the following charts and determine which chart shows the probability distribution for the sum of the two numbers. chart a x 2 3 4 5 6 7 8 9 10 11 12 px one-sixth startfraction 5 over 36 endfraction startfraction 1 over 9 endfraction startfraction 1 over 12 endfraction startfraction 1 over 18 endfraction startfraction 1 over 36 endfraction startfraction 1 over 18 endfraction startfraction 1 over 12 endfraction startfraction 1 over 9 endfraction startfraction 5 over 36 endfraction one-sixth chart b x 2 3 4 5 6 7 8 9 10 11 12 px startfraction 1 over 36 endfraction startfraction 1 over 18 endfraction startfraction 1 over 12 endfraction startfraction 1 over 9 endfraction startfraction 5 over 36 endfraction one-sixth startfraction 5 over 36 endfraction startfraction 1 over 9 endfraction startfraction 1 over 12 endfraction startfraction 1 over 18 endfraction startfraction 1 over 36 endfraction chart c x 2 3 4 5 6 7 8 9 10 11 12 px startfraction 1 over 12 endfraction startfraction 1 over 12 endfraction startfraction 1 over 12 endfraction startfraction 1 over 12 endfraction startfraction 1 over 12 endfraction startfraction 2 over 12 endfraction startfraction 1 over 12 endfraction startfraction 1 over 12 endfraction startfraction 1 over 12 endfraction startfraction 1 over 12 endfraction startfraction 1 over 12 endfraction a. chart

Answer 1

Chart B accurately represents the probability distribution for the sum of two numbers when two dice are rolled, as it correctly assigns probabilities based on the number of ways each sum can occur over the total number of possible outcomes (36).

Step-by-step explanation:

When two dice are rolled, there are indeed 36 equally likely outcomes. If we let x be the sum of the two numbers rolled and p be the probability of the desired sum, we can calculate p for each possible sum of the two dice. Examining the charts given, we need to select which one accurately represents the probability distribution for the sum of two numbers when two dice are rolled. The correct probability for each sum can be worked out by counting the number of ways each sum can be achieved and then dividing by the total number of outcomes, which is 36. For example, the sum of 2 can only be achieved in one way: (1, 1), so p(x=2) is 1/36. Whereas, the sum of 7 can be achieved in six ways: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1), so p(x=7) is 6/36 or simplified to 1/6. By this method, Chart B accurately represents the probability distribution for the sum of the numbers on two dice. It correctly assigns a probability of 1/36 to a sum of 2 and 12, 2/36 (or 1/18) for a sum of 3 and 11, and so on up to a probability of 1/6 for a sum of 7, which is the most common sum.