Two dice are rolled; find the probability that the sum is
a) equal to 1
b) equal to 4
c) less than 13
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a) The sum of two dice cannot be 1 because the minimum sum possible when rolling two dice is 2. Therefore, the probability of the sum being equal to 1 is 0.
b) To find the probability that the sum is equal to 4, we need to enumerate the event when the dice are rolled. The ways to achieve a sum of 4 are (1,3), (2,2), and (3,1). There are a total of 36 possible outcomes when rolling two dice (6 outcomes for the first dice and 6 outcomes for the second dice). Therefore, the probability of the sum being equal to 4 is 3/36 or 1/12.
c) The sum of two dice ranges from 2 to 12. Since the maximum sum possible is 12, any sum less than 13 includes all possible sums. Therefore, the probability of the sum being less than 13 is 1.
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