Question

A box contains 4 red pencils, 3 blue pencils, and 3yellow pencils. What is the probability that a studentrandomly selects a blue pencil, returns the pencil, andthen a second student randomly selects a yellow pencil?

Answer 1

The probability of selecting a pencil of a certain color is given by the amount of pencils of that color over the total number of pencils.

Knowing that, let's first calculate the total number of pencils:

`4+3+3=10`

Then, the probability of selecting a blue pencil is:

`P(B)=(3)/(10)`

And the probability of selecting a yellow pencil is:

`P(Y)=(3)/(10)`

Now, to calculate the probability of both events happening, we just need to multiply the probabilities of each event:

`P(B\text{ and }Y)=P(B)\cdot P(Y)=(3)/(10)\cdot(3)/(10)=(9)/(100)=0.09`

So the probability is 0.09 or 9%.