Two fair dice are thrown together two times. Find the probability of obtaining a sum of seven in the first throw and a sum of four in the second throw.
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Correct Answer: Option
Explanation:
P(a sum of 7) = \(\frac{6}{36}\) and P(a sum of 4) = \(\frac{3}{36}\)
P(a sum of 4) = \(\frac{3}{36}\)
P(a sum of 7 and a sum of 4) = \(\frac{6}{36} \times \frac{3}{36}\) = \(\frac{1}{72}\)
| + | 1 | 2 | 3 | 4 | 5 | 6 |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| 6 | 7 | 8 | 9 | 10 | 11 | 12 |
P(a sum of 7) = \(\frac{6}{36}\) and P(a sum of 4) = \(\frac{3}{36}\)
P(a sum of 4) = \(\frac{3}{36}\)
P(a sum of 7 and a sum of 4) = \(\frac{6}{36} \times \frac{3}{36}\) = \(\frac{1}{72}\)