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Chapter 8: Problem 436

What is the probability of making a 7 in one throw of a pair of dice?

Short Answer

Expert verified
The probability of making a 7 in one throw of a pair of dice is \(\frac{1}{6}\) or approximately 0.1667.

Step by step solution

01

List all possible outcomes (sample space) of throwing two dice

When you throw two dice, both dice have 6 sides each, numbered from 1 to 6. So the possible outcomes are {(1,1), (1,2), (1,3), ..., (6,5), (6,6)}, resulting in a total of 6 x 6 = 36 possible outcomes.
02

Find the favorable outcomes that result in a sum of 7

To find the number of outcomes that result in a sum of 7, we need to look for combinations of numbers 1 through 6 that add up to 7 in the sample space. The combinations are: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). There are 6 favorable outcomes that result in a sum of 7.
03

Calculate the probability

To find the probability of getting a sum of 7 on a single throw of a pair of dice, we divide the number of favorable outcomes (6) by the total number of possible outcomes (36). So the probability is P(7) = \(\frac{6}{36}\).
04

Simplify the probability

The fraction \(\frac{6}{36}\) can be simplified by dividing both the numerator (6) and the denominator (36) by their greatest common factor, which is 6. So the simplified probability of getting a sum of 7 on a single throw of a pair of dice is P(7) = \(\frac{1}{6}\). Thus, the probability of making a 7 in one throw of a pair of dice is \(\frac{1}{6}\) or approximately 0.1667 (rounded to four decimal places).

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