Question

There is 3 red marbles, 7 white marbles, and 5 blue marbles. You draw 3 marbles replacing each one before drawing the next. What is the probability of drawing a red marble, then a blue marble, and then a white marble?

Answer 1

The jar contains 3+7+5=15 marbles in total.

We have to find the probability of the following events:

1. We choose a red marble from the jar that contains 15 marbles in total, 3 of them are red

2. We choose a blue marble from the jar that contains 15 marbles in total, 5 of them are blue

3. We choose a white marble from the jar that contains 15 marbles in total, 7 of them are white

The probability of the first event to happen is:

$P_1=\frac{3}{15}=\frac{1}{5}$

The probability of the second event to happen is:

$P_2=\frac{5}{15}=\frac{1}{3}$

The probability of the third event to happen is:

$P_3=\frac{7}{15}$

The probability of all three events to happen is:

$P=P_1\cdot P_2\cdot P_3=\frac{1}{5}\cdot \frac{1}{3}\cdot \frac{7}{15}=\frac{7}{225}=0.0311$