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:

$P(B)=\frac{3}{10}$

And the probability of selecting a yellow pencil is:

$P(Y)=\frac{3}{10}$

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

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

So the probability is 0.09 or 9%.