I need help with probability

Question

The table shows the outcomes of rolling two number cubes at the same time and finding the product of the two numbers. If Abby rolls two number cubes three hundred times, about how many times would she expect a product greater than 10? Enter your answer in the box.

 

Answer 1

The number of all possible combinations of the two dice is 36.

From those 36 combinations, we have a product greater than 10 when your dice are (2,6) (3,4) (3,5) (3,6) (4,3) (4,4) (4,5) (4,6) (5,3) (5,4) (5,5) (5,6) (6,2) (6,3) (6,4) (6,5) and (6,6). Those are 17 out of 36 possible outcomes.

The probability of a single roll of dice getting a product greater than 10 is 17/36. ≈ 0.4722

The expectation of getting a product greater than 10 in 300 rolls is 300 * (17/36) = 425/3 ≈ 142