emma will roll two number cubes labeled 1 through 6. She will record the sum of the two numbers after each roll. She will roll the two cubes 540 times. How many times should Emma expect the sum to equal 5?

75 times

Step-by-step explanation:

First of all let's ook at the 36 possible outcomes and their sums.

2=1,1

3=1,2 2,1

4=1,3; 2,2; 3,1

5=1,4; 2,3; 3,2; 4,1

6=1,5; 2,4; 3,3; 4,2; 5,1

7=1,6; 2,5; 3,4; 4,3; 5,2; 6,1

8=2,6; 3,5; 4,4; 5,3; 6,2

9=3,6; 4,5; 5,4; 6,3

10=4,6; 5,5; 6,4

11=5,6; 6,5

12=6,6

Looking at the above, there are 4 sums equal to 5 out of a total of 36 sums.

Thus, probability of getting a sum equal to 5 is;

P (5) = 5/36

Now, since the cubes are rolled 540 times, number of times a sum equal to 5 will appear will be;

(5/36) x 540 = 75 times