A and B play 12 games of chess, of which 6 are won by A, 4 are won by B, and 2 end in draw. They agree to play a match consisting of 3 games. Find the probability that: i) A wins all the 3 games ii) 2 games end in draw iii) A and B win alternatively iv) B wins at least one game.

A and B play 12 games of chess, of which 6 are won by A, 4 are won by B, and 2 end in draw. They agree to play a match consisting of 3 games. Find the probability that: i) A wins all the 3 games ii) 2 games end in draw iii) A and B win alternatively iv) B wins at least one game.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

A and B play 12 games of chess, of which 6 are
won by A, 4 are won by B, and 2 end in draw.
They agree to play a match consisting of 3
games. Find the probability that:
i) A wins all the 3 games
ii) 2 games end in draw
iii) A and B win alternatively
iv) B wins at least one game.

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Step 2: Find probability of winning single game and game end on draw

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Step 3: Find the probability that A wins all 3 games:

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Step 4: Find the probability that two games end in a draw

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Step 5: Find the probability of A and B winning game alternatively

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Step 6: Find the probability that B wins at least one game

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