Solution Found!
An urn contains 12 balls, of which 4 are white. Three
Chapter 3, Problem 84P(choose chapter or problem)
Problem 84P
An urn contains 12 balls, of which 4 are white. Three players—A, B, and C—successively draw from the urn, A first, then B, then C, then A, and so on. The winner is the first one to draw a white ball. Find the probability of winning for each player if
(a) each ball is replaced after it is drawn;
(b) the balls that arc withdrawn are not replaced.
Questions & Answers
QUESTION:
Problem 84P
An urn contains 12 balls, of which 4 are white. Three players—A, B, and C—successively draw from the urn, A first, then B, then C, then A, and so on. The winner is the first one to draw a white ball. Find the probability of winning for each player if
(a) each ball is replaced after it is drawn;
(b) the balls that arc withdrawn are not replaced.
ANSWER:
Step 1 of 6
Given that urn contains 12 balls in that 4 white
There are 3 players A, B and C
First chance is for A , 2nd chance for B and 3rd chance for C to pick ball from urn
Who gets white ball first that person is winner
a) we have to find the probability of winning each person with replacement
Probability of getting white ball is 4/12=1/3
Probability of A winning =Probability of A drawing white in his 1st , 2nd, 3rd draw
=
=
=
=
=
Hence probability of A winning with replacement is 9/19