Question

Vanessa has two bags that contain slips of paper. One bag has 4 slips of paper that are numbered 2, 3, 4, and 5. The other bag has 4 slips of paper that are numbered 3, 4, 5, and 6.

Vanessa chooses one slip of paper from each bag without looking.

The random variable X is the product of the numbers on the slips of paper.

What is P(12 ≤ X ≤ 15)?



Enter your answer, in simplest fraction form, in the box.

Answer 1

5/16

Explanation:

If Vanessa pulls out a 2 from the first bag, then the possibilities based on the second bag are:

X = 2*3 = 6

X = 2*4 = 8

X = 2*5 = 10

X = 2*6 = 12

Repeat this for the other values from the first bag. If she pulls a 3, the possibilities are:

X = 3*3 = 9

X = 3*4 = 12

X = 3*5 = 15

X = 3*6 = 18

If she pulls a 4:

X = 4*3 = 12

X = 4*4 = 16

X = 4*5 = 20

X = 4*6 = 24

And finally, if she pulls a 5:

X = 5*3 = 15

X = 5*4 = 20

X = 5*5 = 25

X = 5*6 = 30

Of the 16 total combinations, 5 are greater than or equal to 12 and less than or equal to 15.

Therefore, P(12 ≤ X ≤ 15) = 5/16.