Question

1. you have 3 black, 1 green, and 2 blue pens in a drawer. suppose you reach into the drawer without looking and choose a pen, replace it, and then choose another pen. what is the probability of randomly choosing a green pen first and then choosing a second pen that is blue?

Explanation:

Step1: Calculate probability of choosing green pen first

The total number of pens is $3 + 1+2=6$. The probability of choosing a green pen on the first - draw, since there is 1 green pen out of 6 pens, is $P(\text{green})=\frac{1}{6}$.

Step2: Calculate probability of choosing blue pen second

Since the pen is replaced, the total number of pens is still 6. There are 2 blue pens, so the probability of choosing a blue pen on the second - draw is $P(\text{blue})=\frac{2}{6}=\frac{1}{3}$.

Step3: Calculate the joint probability

Since the two events are independent (because of replacement), the probability of both events occurring is the product of their individual probabilities. So $P(\text{green then blue})=P(\text{green})\times P(\text{blue})=\frac{1}{6}\times\frac{1}{3}=\frac{1}{18}$.

Answer:

$\frac{1}{18}$