Question

Suppose you have a box with 3 blue marbles, 2 red marbles, and 4 yellow marbles. You are going to pull out one marble, record its color, put it back in the box and draw another marble. What is the probability of pulling out a red marble followed by a blue marble?

• A. $\frac{8}{81}$
• B. $\frac{2}{27}$
• C. $\frac{1}{27}$
• D. $\frac{1}{9}$

Answer 1

The correct option is B $\frac{2}{27}$

Since we are putting the ball back, the events are independent.
We want to find the probability of the event Red in the first attempt and blue in the second attempt.
$P(R\cap B)=P\left(R\right)P\left(B\right)P\left(red\right)=\frac{2}{9}P\left(blue\right)=\frac{3}{9}\Rightarrow P(R\cap B)=P\left(R\right)P\left(B\right)=\frac{2}{9}\times \frac{3}{9}=\frac{2}{27}$