Question

Michelle has 2 number cubes, each labeled 1 to 6. If Michelle rolls each number cube 200 times, about how many times would she expect to roll a sum of 4 or less?

Answer 1

33 times

Explanation:

Total outcomes of rolling two cubes :

[1,1] ; [1,2] ; [1,3] ; [1,4] ; [1,5] ; [1,6]

[2,1] ; [2,2] ; [2,3] ; [2,4] ; [2,5] ; [2,6]

[3,1] ; [3,2] ; [3,3] ; [3,4] ; [3,5] ; [3,6]

[4,1] ; [4,2] ; [4,3] ; [4,4] ; [4,5] ; [4,6]

[5,1] ; [5,2] ; [5,3] ; [5,4] ; [5,5] ; [5,6]

[6,1] ; [6,2] ; [6,3] ; [6,4] ; [6,5] ; [6,6]

So, total no. of outcomes of rolling two cubes = 36

Favorable outcomes : roll a sum of 4 or less i.e. sum of 2,3,4

So, favorable outcomes :[1,1] ; [1,2] ; [2,1] ; [1,3] ; [3,1] ; [2,2] = 6

Thus the probability of getting a sum of 4 or less :

=
`\frac{\text{Favorable outcomes}}{\text{total outcomes}}`

=
`(6)/(36)`

=
`(1)/(6)`

So, probability of getting sum of 4 or less is 1/6

Since he rolls each number cube 200 times

So, she expect to get a sum of 4 or less =
`200*(1)/(6)` times

= 33.33

So, she would expect to roll a sum of 4 or less for 33 times .