A box contains 6 red balls, 7 yellow balls, and 2 green balls. All the balls are the same except for their color. Jaime picks a ball from the box, records the color, then returns the ball to the box. He does this 3 times.

Question

What is the probability that all three balls that Jaime picked were red?

Answer 1

The probability of picking a red ball on each individual draw is the same: $\frac{6}{6+7+2}=\frac{6}{15}=\boxed{\frac{2}{5}}$. Since the three draws are independent events, we multiply the probabilities. \[\left(\frac{2}{5}\right)^{\!3}=\frac{2^3}{5^3}=\frac{8}{125}.\]