A bag contains 1 red ball and 2 white balls. One ball is randomly selected from the bag and then returned. What is the probability that exactly one of the first five balls selected is white?

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Answer 1 · 2017-01-14T09:43:07

The answer is #=10/243#

This is a binomial distribution.

The probability of getting 1 white ball on one draw is #P_w=2/3#

The probability of not getting a white ball on one draw#=1-P_w=1/3#

The probability of getting 1 white ball on the five draws is

#= ((5),(1)) * (2/3) *(1/3)^4 # where

#((5),(1))=(5!)/((5-1)!(1!))=5#

Therefore,

#P#(1 out of 5) #=5*2/3*(1/3)^4=10/243#