Question

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 $\bar{A}$, 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Find the probability of winning for each player if (a) each ball is replaced after it is drawn; (b) the balls that are withdrawn are not replaced.

          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 $\bar{A}$, 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(b) the balls that are withdrawn are not replaced.

Added by John M.

Probability with Applications in Engineering, Science, and Technology

Matthew A. Carlton • Jay L. Devore 2nd Edition

Instant Answer

Solved by Expert Adi S

05/25/2024

Step 1

The probability of player A winning on their first turn is the probability of drawing a white ball, which is $\frac{4}{12} = \frac{1}{3}$. If player A doesn't win on their first turn, they have another chance to win after players B and C have taken their turns. Show more…

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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Find the probability of winning for each player if (a) each ball is replaced after it is drawn; (b) the balls that are withdrawn are not replaced.