Ethan rolls two number cubes with sides numbered 1 through 6. If he rolls the pair of number cubes 300 times, how many times would he expect to roll a sum of 6?

Question

This assignment is due pretty soon so I need an answer quick.

Answer 1

ways you can get a total 6 are:

1 and 5

5 and 1

2 and 4

4 and 2

3 and 3

that's 5 ways to get 6

total ways the dice can turn up are:

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12

11 different possible outcomes

6^2 = 36 ways the outcomes can turn up

one way to get 2 1/36 chance

2 ways to get 3 2/36 chance

3 ways to get 4 3/36 "

4 ways to get 5 4/36

5 ways to get 6 5/36 chance of getting a 6 sum of the two cubes

6 ways to get 7 6/36

5 ways to get 8 5/36

4 ways to get 9 4/36

3 ways to get 10 3/36

2 ways to get 11 2/36

1 way to get 12 1/36

5/36 chance of 6

300 rolls of the cubes has 300(5/36) = 750/18 = 250/6 = 41 1/3. expected number of 6's is 41 in 300 rolls

36 total ways the cubes turn up