Two regular 6-sided dice are tossed. Compute the probability that the sum of the pips on the upward faces of the 2 dice is at least 10. (See the figure below for the sample space of this experiment. Enter your probability as a fraction.)
Question
Two regular 6-sided dice are tossed. Compute the probability that the sum of the pips on the upward faces of the 2 dice is at least 10. (See the figure below for the sample space of this experiment. Enter your probability as a fraction.)
Solution
To solve this problem, we first need to understand the total number of possible outcomes when two dice are rolled. Since each die has 6 faces, the total number of outcomes is 6*6 = 36.
Next, we need to find out the number of outcomes where the sum of the pips is at least 10. The combinations that satisfy this condition are (4,6), (5,5), (5,6), (6,4), (6,5), and (6,6). So, there are 6 such combinations.
However, since each combination can occur in two ways (for example, (4,6) can occur as 4 on the first die and 6 on the second, or 6 on the first die and 4 on the second), we need to multiply the number of combinations by 2. But, the combination (5,5) and (6,6) can occur in only one way. So, the total number of favorable outcomes is 2*4 + 2 = 10.
Finally, the probability of the sum of the pips being at least 10 is the number of favorable outcomes divided by the total number of outcomes, which is 10/36 = 5/18.
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