Get the complete, step-by-step math solution for: "Two dice are thrown at the same time and the product of the numbers appearing on them is noted. The probability that the product of the numbers lies b...". Powered by SolveForX AI math tutor.
Step 1: Determine the sample space
When two dice are thrown, each die has 6 possible outcomes (1, 2, 3, 4, 5, 6). The total number of possible outcomes in the sample space is the product of the outcomes for each die.
Step 2: List outcomes with product between 8 and 13
We need to find pairs of numbers whose product is greater than 8 and less than 13. We list all such pairs: (2,4) product is 8 (not included), (2,5) product is 10, (2,6) product is 12, (3,3) product is 9, (3,4) product is 12, (4,2) product is 8 (not included), (4,3) product is 12, (5,2) product is 10, (6,2) product is 12. The products must be strictly between 8 and 13, so 8 and 13 are excluded. The favorable outcomes are those with products 9, 10, 11, 12.