# A box contains 5 plain pencils and 3 pens. A second box contains 2 color pencils and 2 crayons . One

Discussion in 'Calculator Requests' started by math_celebrity, Apr 19, 2020.

Tags:
1. ### math_celebrityAdministratorStaff Member

A box contains 5 plain pencils and 3 pens. A second box contains 2 color pencils and 2 crayons. One item from each box is chosen at random. What is the probability that a plain pencil from the first box and a color pencil from the second box are selected

Calculate the probability of a plain pencil in the first box:
P(plain pencil in the first box) = Total Pencils / Total Objects
P(plain pencil in the first box) = 5 pencils / (5 pencils + 3 pens)
P(plain pencil in the first box) = 5/8

Calculate the probability of a color pencil in the first box:
P(color in the second box) = Total Pencils / Total Objects
P(color in the second box) = 2 pencils / (2 pencils + 2 crayons)
P(color in the second box) = 2/4

We can simplify this. Type 2/4 into our search engine and we get 1/2

Now the problem asks for the probability that a plain pencil from the first box and a color pencil from the second box are selected.

Since each event is independent, we multiply them together to get our answer:
P(plain pencil in the first box, color in the second box) = P(plain pencil in the first box) * P(color in the second box)
P(plain pencil in the first box, color in the second box) = 5/8 * 1/2
P(plain pencil in the first box, color in the second box) = 5/16