Final answer:
The probability that the sum of the spots on two throws of a six-sided die is divisible by both 2 and 3 is 1/6, as there are 6 favorable outcomes out of a total of 36 possible outcomes.
Step-by-step explanation:
A student has asked what is the probability that the sum of the spots on two throws of a die is divisible by both 2 and 3. To solve this, we consider the sample space when a six-sided die is rolled twice, which has 36 possible outcomes. Since we want the sum to be divisible by both 2 and 3, the sum must be divisible by 6 (because 6 is the least common multiple of 2 and 3). The sums that are divisible by 6 are 6, 12, 18, 24, 30, and 36. Of these, only 6 and 12 are possible sums of two dice throws (since the highest sum we can get by rolling two six-sided dice is 12).
The possible pairs (first throw, second throw) that add up to 6 are (1,5), (2,4), (3,3), (4,2), and (5,1). Similarly, the pairs that add up to 12 are (6,6).
This gives us a total of 6 favorable outcomes.
The probability is therefore the number of favorable outcomes divided by the total number of outcomes in the sample space (36), which is 6/36, or simplified, 1/6.