Question

Three balls are drawn from a box containing 6 red marbles, 4 white marbles and 5 blue marbles. Find the probability that they are drawn in the order: red, white, and blue if each ball is drawn with replacement
a) 8/225
b) 1/225
c) 4/225
d) 6/225

Answer 1

Answer on Question #51598 – Math – Statistics and Probability

Question

Three balls are drawn from a box containing 6 red marbles, 4 white marbles and 5 blue marbles. Find the probability that they are drawn in the order: red, white, and blue if each ball is drawn with replacement.

a) $\frac{8}{225}$

b) $\frac{1}{225}$

c) $\frac{4}{225}$

d) $\frac{6}{225}$

Solution

The probability to draw a red marble is equal to $\frac{6}{6 + 4 + 5} = \frac{6}{15} = \frac{2}{5}$. You then put that red marble back into the box. The probability to draw a white marble is equal to $\frac{4}{15}$. You then put that white marble back into the box. The probability to draw a blue marble is equal to $\frac{5}{15} = \frac{1}{3}$. Since each ball is drawn with replacement and these three events are independent, we use the multiplication rule. The required probability is equal to $P = \frac{2}{5} \cdot \frac{4}{15} \cdot \frac{1}{3} = \frac{8}{225}$.

Answer: a) $\frac{8}{225}$

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