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Chapter 23: Problem 9

Two fair dice are thrown. Calculate the probability that the total is (a) 9 (b) 13 (c) more than 9

Short Answer

Expert verified
Answer: (a) The probability of rolling a total of 9 is 1/9. (b) The probability of rolling a total of 13 is 0. (c) The probability of rolling a total greater than 9 is 1/6.

Step by step solution

01

Determine the total number of outcomes

When two dice are thrown, there are 6 sides on each die, so there are 6 x 6 = 36 possible outcomes.
02

Count the outcomes that meet the criteria for each part

For each part, we'll count the number of outcomes that meet the specific condition: (a) To get a total of 9, we can have the following outcomes: (3,6), (4,5), (5,4), and (6,3). There are 4 outcomes in this case. (b) It's impossible to get a total of 13 with two dice, as the maximum possible roll is 12 (6 + 6). There are 0 outcomes in this case. (c) To get a total greater than 9, we can have the following outcomes: (4,6), (5,5), (5,6), (6,4), (6,5), and (6,6). There are 6 outcomes in this case.
03

Calculate the probability for each part

Now that we know the number of outcomes that meet the specific condition for each part, we can calculate the probability by dividing that number by the total number of outcomes (36). (a) P(total = 9) = 4/36 = 1/9 (b) P(total = 13) = 0/36 = 0 (c) P(total > 9) = 6/36 = 1/6 The probabilities for each part are as follows: (a) The probability that the total is 9: 1/9 (b) The probability that the total is 13: 0 (c) The probability that the total is more than 9: 1/6

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