A bag contains 5 red balls and 2 black balls. We draw 5 balls, with each one replaced before the next is drawn. What is the probability that 3 balls drawn will be red? Round your answer to six decimal places.
A)Pr(3 Red) = 0.600000
B)Pr(3 Red) = 0.014875
C)Pr(3 Red) = 0.297495
D)Pr(3 Red) = 0.002479
E)Pr(3 Red) = 0.578330

Question

A bag contains 5 red balls and 2 black balls. We draw 5 balls, with each one replaced before the next is drawn. What is the probability that 3 balls drawn will be red? Round your answer to six decimal places. ​
A)Pr(3 Red) = 0.600000
B)Pr(3 Red) = 0.014875
C)Pr(3 Red) = 0.297495
D)Pr(3 Red) = 0.002479
E)Pr(3 Red) = 0.578330

Quizplus · Accepted Answer

The probability of drawing a red ball in each individual draw is 5/7. Since we are replacing the ball after each draw, the probability remains the same for each draw. Using the binomial probability formula with n=5 (number of trials/draws) and p=5/7 (probability of success), we get:
P(3 red) = (5 choose 3) * (5/7)^3 * (2/7)^2 = 0.297495
Rounding to six decimal places, we get 0.297495 as the answer, which matches with choice C.

A Bag Contains 5 Red Balls and 2 Black Balls