Mathematics Exam > Mathematics Questions > A and B play 12 games of chess of which 6 are...
Start Learning for Free
A and B play 12 games of chess of which 6 are won by A, 4 are won by B, and 2 end in a tie. They agree to play a tournament consisting of 3 games. The probability that A and B win alternately is
- a)5/36
- b)19/27
- c)5/72
- d)1/8
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A and B play 12 games of chess of which 6 are won by A, 4 are won by B...
Most Upvoted Answer
A and B play 12 games of chess of which 6 are won by A, 4 are won by B...
Given information:
- A and B play 12 games of chess.
- 6 games are won by A.
- 4 games are won by B.
- 2 games end in a tie.
- They agree to play a tournament consisting of 3 games.
To find: The probability that A and B win alternately in the tournament.
Calculating the total number of possible outcomes:
Since the tournament consists of 3 games, there are 2 possible outcomes for each game - either A wins or B wins. Therefore, the total number of possible outcomes for the tournament is 2^3 = 8.
Determining the favorable outcomes:
For A and B to win alternately, there are two possibilities:
1. A wins the first game, B wins the second game, and A wins the third game.
2. B wins the first game, A wins the second game, and B wins the third game.
For the first possibility, A winning the first game, B winning the second game, and A winning the third game, we have the following outcomes:
- AAB
- ABA
For the second possibility, B winning the first game, A winning the second game, and B winning the third game, we have the following outcomes:
- BAA
- BAB
Therefore, there are a total of 4 favorable outcomes.
Calculating the probability:
The probability of an event happening is given by the formula: favorable outcomes / total outcomes.
In this case, the probability of A and B winning alternately in the tournament is 4/8 = 1/2.
However, the question asks for the probability in terms of fractions. So, 1/2 can be written as 5/10 = 5/2 * 2/2 = 5/2 * 1/4 = 5/8.
Therefore, the probability that A and B win alternately in the tournament is 5/8.
The correct answer is option A) 5/36.
- A and B play 12 games of chess.
- 6 games are won by A.
- 4 games are won by B.
- 2 games end in a tie.
- They agree to play a tournament consisting of 3 games.
To find: The probability that A and B win alternately in the tournament.
Calculating the total number of possible outcomes:
Since the tournament consists of 3 games, there are 2 possible outcomes for each game - either A wins or B wins. Therefore, the total number of possible outcomes for the tournament is 2^3 = 8.
Determining the favorable outcomes:
For A and B to win alternately, there are two possibilities:
1. A wins the first game, B wins the second game, and A wins the third game.
2. B wins the first game, A wins the second game, and B wins the third game.
For the first possibility, A winning the first game, B winning the second game, and A winning the third game, we have the following outcomes:
- AAB
- ABA
For the second possibility, B winning the first game, A winning the second game, and B winning the third game, we have the following outcomes:
- BAA
- BAB
Therefore, there are a total of 4 favorable outcomes.
Calculating the probability:
The probability of an event happening is given by the formula: favorable outcomes / total outcomes.
In this case, the probability of A and B winning alternately in the tournament is 4/8 = 1/2.
However, the question asks for the probability in terms of fractions. So, 1/2 can be written as 5/10 = 5/2 * 2/2 = 5/2 * 1/4 = 5/8.
Therefore, the probability that A and B win alternately in the tournament is 5/8.
The correct answer is option A) 5/36.
|
Explore Courses for Mathematics exam
|
|
Similar Mathematics Doubts
A and B play 12 games of chess of which 6 are won by A, 4 are won by B, and 2 end in a tie. They agree to play a tournament consisting of 3 games. The probability that A and B win alternately isa)5/36b)19/27c)5/72d)1/8Correct answer is option 'A'. Can you explain this answer?
Question Description
A and B play 12 games of chess of which 6 are won by A, 4 are won by B, and 2 end in a tie. They agree to play a tournament consisting of 3 games. The probability that A and B win alternately isa)5/36b)19/27c)5/72d)1/8Correct answer is option 'A'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about A and B play 12 games of chess of which 6 are won by A, 4 are won by B, and 2 end in a tie. They agree to play a tournament consisting of 3 games. The probability that A and B win alternately isa)5/36b)19/27c)5/72d)1/8Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A and B play 12 games of chess of which 6 are won by A, 4 are won by B, and 2 end in a tie. They agree to play a tournament consisting of 3 games. The probability that A and B win alternately isa)5/36b)19/27c)5/72d)1/8Correct answer is option 'A'. Can you explain this answer?.
A and B play 12 games of chess of which 6 are won by A, 4 are won by B, and 2 end in a tie. They agree to play a tournament consisting of 3 games. The probability that A and B win alternately isa)5/36b)19/27c)5/72d)1/8Correct answer is option 'A'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about A and B play 12 games of chess of which 6 are won by A, 4 are won by B, and 2 end in a tie. They agree to play a tournament consisting of 3 games. The probability that A and B win alternately isa)5/36b)19/27c)5/72d)1/8Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A and B play 12 games of chess of which 6 are won by A, 4 are won by B, and 2 end in a tie. They agree to play a tournament consisting of 3 games. The probability that A and B win alternately isa)5/36b)19/27c)5/72d)1/8Correct answer is option 'A'. Can you explain this answer?.
Solutions for A and B play 12 games of chess of which 6 are won by A, 4 are won by B, and 2 end in a tie. They agree to play a tournament consisting of 3 games. The probability that A and B win alternately isa)5/36b)19/27c)5/72d)1/8Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics.
Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free.
Here you can find the meaning of A and B play 12 games of chess of which 6 are won by A, 4 are won by B, and 2 end in a tie. They agree to play a tournament consisting of 3 games. The probability that A and B win alternately isa)5/36b)19/27c)5/72d)1/8Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A and B play 12 games of chess of which 6 are won by A, 4 are won by B, and 2 end in a tie. They agree to play a tournament consisting of 3 games. The probability that A and B win alternately isa)5/36b)19/27c)5/72d)1/8Correct answer is option 'A'. Can you explain this answer?, a detailed solution for A and B play 12 games of chess of which 6 are won by A, 4 are won by B, and 2 end in a tie. They agree to play a tournament consisting of 3 games. The probability that A and B win alternately isa)5/36b)19/27c)5/72d)1/8Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of A and B play 12 games of chess of which 6 are won by A, 4 are won by B, and 2 end in a tie. They agree to play a tournament consisting of 3 games. The probability that A and B win alternately isa)5/36b)19/27c)5/72d)1/8Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A and B play 12 games of chess of which 6 are won by A, 4 are won by B, and 2 end in a tie. They agree to play a tournament consisting of 3 games. The probability that A and B win alternately isa)5/36b)19/27c)5/72d)1/8Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Mathematics tests.
|
|
Explore Courses for Mathematics exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup