Question

# An urn contains 5 red and 9 pink balls. Four balls are randomly drawn from the...

An urn contains 5 red and 9 pink balls. Four balls are randomly drawn from the urn in succession, with replace

ment. That is, after each draw, the selected ball is returned to the urn. What is the probability that all 4 balls drawn from the urn are red? Round your answer to three decimal places.

Solution: There are total (5+9) = 14 balls in the urn.

Since there are 5 red balls,so the probability of drawing a red ball each time = 5/14.

Also, since the drawing is independent as it has been made with replacement, the event of of drawing a red ball in every four attempts is independent of one another.

Thus, probability of getting red ball in 1st draw and in 2nd draw and in 3rd draw and in 4th draw can be written as--

P(getting red ball in 1st draw) * P(getting red ball in 2nd draw) * P(getting red ball in 3rd draw) * P(getting red ball in 4th draw) = (5/14) * (5/14) * (5/14) * (5/14) = 625 / 38416 = 0.016 ( rounded to three decimal places)