Two fair dice are rolled. Find the probability that the sum of the two numbers is not greater than 5 .
A. $\frac{13}{18}$
B. $\frac{5}{18}$
C. $\frac{1}{6}$
D. $\frac{1}{3}$
Answer
The final answer is approximately 0.278, which is not exactly equal to any of the options given in the question. However, it is closest to \(\frac{5}{18}\), which is approximately 0.277. So, the closest answer is \(\boxed{\frac{5}{18}}\).
Step 1 ：When two fair dice are rolled, the total number of outcomes is 36. This is because there are 6 outcomes for the first die and 6 for the second die.
Step 2 ：We need to find the number of outcomes where the sum of the two numbers is not greater than 5. This includes the sums 2, 3, 4, and 5.
Step 3 ：The number of outcomes for each of these sums are as follows: \[\text{sum}_2 = 1, \text{sum}_3 = 2, \text{sum}_4 = 3, \text{sum}_5 = 4\]
Step 4 ：So, the total number of outcomes where the sum of the two numbers is not greater than 5 is \[\text{total} = 1 + 2 + 3 + 4 = 10\]
Step 5 ：The probability of this event is the ratio of the number of favorable outcomes to the total number of outcomes. So, the probability is \[\text{probability} = \frac{\text{total}}{\text{total outcomes}} = \frac{10}{36} = 0.2777777777777778\]
Step 6 ：The final answer is approximately 0.278, which is not exactly equal to any of the options given in the question. However, it is closest to \(\frac{5}{18}\), which is approximately 0.277. So, the closest answer is \(\boxed{\frac{5}{18}}\).
