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Chapter 2: Problem 97

Determine the probability of getting 6 or 7 in a toss of two dice.

Short Answer

Expert verified
The probability of getting a sum of 6 or 7 when tossing two dice is \(\frac{11}{36}\).

Step by step solution

01

Calculate the total possible outcomes

When tossing two dice, each die has six faces, numbered 1 to 6. The total possible outcomes can be found by multiplying the number of faces on each die. That means, \[6 \times 6 = 36\] There are 36 possible outcomes when tossing two dice.
02

Identify the favorable outcomes

To find the probability of getting a sum of 6 or 7, we need to identify all the possible pairs of outcomes that result in a sum of either 6 or 7. For a sum of 6, we have: (1, 5), (2, 4), (3, 3), (4, 2), (5, 1) There are 5 possible outcomes that result in a sum of 6. For a sum of 7, we have: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) There are 6 possible outcomes that result in a sum of 7. Now, we can add the number of outcomes for both sums 6 and 7 to find the total favorable outcomes. \[5 + 6 = 11\]
03

Calculate the probability

The probability of getting a sum of 6 or 7 can be calculated by dividing the number of favorable outcomes by the total possible outcomes: \[\frac{Number\,of\,favorable\,outcomes}{Total\,possible\,outcomes} = \frac{11}{36}\] So the probability of getting a sum of 6 or 7 when tossing two dice is \(\frac{11}{36}\).

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