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Chapter 7: Problem 18

A pair of fair dice is rolled. What is the probability that the number landing uppermost on the first die is a 4 if it is known that the sum of the numbers landing uppermost is \(7 ?\)

Short Answer

Expert verified
The probability that the number landing uppermost on the first die is a 4, given that the sum of the numbers landing uppermost is 7, is \(\frac{1}{6}\).

Step by step solution

01

Determine the number of favorable outcomes

We need to find the total number of outcomes where the first die shows 4, and the sum of the two dice is 7. There is only one such outcome, when the first die is a 4 and the second die is a 3 (4+3=7).
02

Determine the number of possible outcomes for the given condition

To find the number of possible outcomes where the sum is 7, consider all the pairs of numbers on two dice that add up to 7. There are the following possibilities: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1). There are 6 possible outcomes where the sum of the two dice is 7.
03

Calculate the probability

We can calculate the probability by dividing the number of favorable outcomes by the number of possible outcomes for the given condition, which is: \[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Number of possible outcomes}} = \frac{1}{6} \] So, the probability that the number landing uppermost on the first die is a 4, given that the sum of the numbers landing uppermost is 7, is \(\frac{1}{6}\).

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Most popular questions from this chapter

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