An urn contains 9 pink and 6 red balls. Five balls are randomly drawn from the urn in succession, with replacement. That is, after each draw, the selected ball is returned to the urn. What is the probability that all 5 balls drawn from the urn are pink? Round your answer to three decimal places.

To find the probability that all 5 balls drawn from the urn are pink, we start by calculating the total number of balls in the urn. There are 9 pink balls and 6 red balls, which gives us a total of 15 balls. The probability of drawing a pink ball in one draw is the number of pink balls divided by the total number of balls: \[ P(\text{pink}) = \frac{9}{15} = \frac{3}{5} \] Since the draws are conducted with replacement, the probability remains constant for each draw. Thus, the probability of drawing 5 pink balls in a row is: \[ P(\text{5 pink}) = \left(\frac{3}{5}\right)^5 = \frac{243}{3125} \] Calculating this gives approximately: \[ \frac{243}{3125} \approx 0.07776 \] Rounding to three decimal places, the probability that all 5 balls drawn from the urn are pink is: **0.078**