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Consider 3 coins having probability of obtaining head in a single trial as 1/4,1/2,3/4 respectively.a player select one of these three coins at random .if the player tosses the selected coin 5 times independently.then what is the probability of obtaining 2 tails in 5 tosses?
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Consider 3 coins having probability of obtaining head in a single tria...
Random selection of a coin:
When the player selects one of the three coins at random, each coin has an equal probability of being selected. This means that the probability of selecting each coin is 1/3.
Tossing the selected coin 5 times:
Since the player is tossing the selected coin independently 5 times, each toss is considered a separate and independent event. The result of one toss does not affect the result of another toss.
Probabilities of obtaining tails for each coin:
The probability of obtaining tails for each coin can be calculated as follows:
- Coin 1: The probability of obtaining tails is 1 - probability of obtaining heads = 1 - 1/4 = 3/4.
- Coin 2: The probability of obtaining tails is 1 - probability of obtaining heads = 1 - 1/2 = 1/2.
- Coin 3: The probability of obtaining tails is 1 - probability of obtaining heads = 1 - 3/4 = 1/4.
Probability of obtaining 2 tails in 5 tosses:
To calculate the probability of obtaining 2 tails in 5 tosses, we need to consider all possible combinations of obtaining 2 tails.
There are different ways to obtain 2 tails in 5 tosses:
- TTTTH: The probability of this combination is (1/4)^4 * (3/4)^1 = 81/1024.
- TTTHT: The probability of this combination is (1/4)^3 * (3/4)^2 = 27/1024.
- TTTHH: The probability of this combination is (1/4)^2 * (3/4)^3 = 9/1024.
- THTTH: The probability of this combination is (1/2)^1 * (1/4)^3 * (3/4)^1 = 9/1024.
- THTHT: The probability of this combination is (1/2)^1 * (1/4)^2 * (3/4)^2 = 9/1024.
- THHTT: The probability of this combination is (1/2)^1 * (1/4)^1 * (3/4)^3 = 27/1024.
- HTTTH: The probability of this combination is (1/2)^1 * (3/4)^1 * (1/4)^3 = 9/1024.
- HTTHT: The probability of this combination is (1/2)^1 * (3/4)^2 * (1/4)^2 = 9/1024.
- HHTTT: The probability of this combination is (1/2)^1 * (3/4)^3 * (1/4)^1 = 27/1024.
- HHTTH: The probability of this combination is (1/2)^1 * (3/4)^2 * (1/4)^2 = 9/1024.
- HHHTT: The probability of this combination is (1/2)^1 * (3/4)^1 * (1/4)^3 = 9/1024.
- HTHHT: The probability of this combination is (1/2)^1 * (1/4)^1
When the player selects one of the three coins at random, each coin has an equal probability of being selected. This means that the probability of selecting each coin is 1/3.
Tossing the selected coin 5 times:
Since the player is tossing the selected coin independently 5 times, each toss is considered a separate and independent event. The result of one toss does not affect the result of another toss.
Probabilities of obtaining tails for each coin:
The probability of obtaining tails for each coin can be calculated as follows:
- Coin 1: The probability of obtaining tails is 1 - probability of obtaining heads = 1 - 1/4 = 3/4.
- Coin 2: The probability of obtaining tails is 1 - probability of obtaining heads = 1 - 1/2 = 1/2.
- Coin 3: The probability of obtaining tails is 1 - probability of obtaining heads = 1 - 3/4 = 1/4.
Probability of obtaining 2 tails in 5 tosses:
To calculate the probability of obtaining 2 tails in 5 tosses, we need to consider all possible combinations of obtaining 2 tails.
There are different ways to obtain 2 tails in 5 tosses:
- TTTTH: The probability of this combination is (1/4)^4 * (3/4)^1 = 81/1024.
- TTTHT: The probability of this combination is (1/4)^3 * (3/4)^2 = 27/1024.
- TTTHH: The probability of this combination is (1/4)^2 * (3/4)^3 = 9/1024.
- THTTH: The probability of this combination is (1/2)^1 * (1/4)^3 * (3/4)^1 = 9/1024.
- THTHT: The probability of this combination is (1/2)^1 * (1/4)^2 * (3/4)^2 = 9/1024.
- THHTT: The probability of this combination is (1/2)^1 * (1/4)^1 * (3/4)^3 = 27/1024.
- HTTTH: The probability of this combination is (1/2)^1 * (3/4)^1 * (1/4)^3 = 9/1024.
- HTTHT: The probability of this combination is (1/2)^1 * (3/4)^2 * (1/4)^2 = 9/1024.
- HHTTT: The probability of this combination is (1/2)^1 * (3/4)^3 * (1/4)^1 = 27/1024.
- HHTTH: The probability of this combination is (1/2)^1 * (3/4)^2 * (1/4)^2 = 9/1024.
- HHHTT: The probability of this combination is (1/2)^1 * (3/4)^1 * (1/4)^3 = 9/1024.
- HTHHT: The probability of this combination is (1/2)^1 * (1/4)^1
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Consider 3 coins having probability of obtaining head in a single trial as 1/4,1/2,3/4 respectively.a player select one of these three coins at random .if the player tosses the selected coin 5 times independently.then what is the probability of obtaining 2 tails in 5 tosses?
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Consider 3 coins having probability of obtaining head in a single trial as 1/4,1/2,3/4 respectively.a player select one of these three coins at random .if the player tosses the selected coin 5 times independently.then what is the probability of obtaining 2 tails in 5 tosses? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Consider 3 coins having probability of obtaining head in a single trial as 1/4,1/2,3/4 respectively.a player select one of these three coins at random .if the player tosses the selected coin 5 times independently.then what is the probability of obtaining 2 tails in 5 tosses? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider 3 coins having probability of obtaining head in a single trial as 1/4,1/2,3/4 respectively.a player select one of these three coins at random .if the player tosses the selected coin 5 times independently.then what is the probability of obtaining 2 tails in 5 tosses?.
Consider 3 coins having probability of obtaining head in a single trial as 1/4,1/2,3/4 respectively.a player select one of these three coins at random .if the player tosses the selected coin 5 times independently.then what is the probability of obtaining 2 tails in 5 tosses? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Consider 3 coins having probability of obtaining head in a single trial as 1/4,1/2,3/4 respectively.a player select one of these three coins at random .if the player tosses the selected coin 5 times independently.then what is the probability of obtaining 2 tails in 5 tosses? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider 3 coins having probability of obtaining head in a single trial as 1/4,1/2,3/4 respectively.a player select one of these three coins at random .if the player tosses the selected coin 5 times independently.then what is the probability of obtaining 2 tails in 5 tosses?.
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Consider 3 coins having probability of obtaining head in a single trial as 1/4,1/2,3/4 respectively.a player select one of these three coins at random .if the player tosses the selected coin 5 times independently.then what is the probability of obtaining 2 tails in 5 tosses?, a detailed solution for Consider 3 coins having probability of obtaining head in a single trial as 1/4,1/2,3/4 respectively.a player select one of these three coins at random .if the player tosses the selected coin 5 times independently.then what is the probability of obtaining 2 tails in 5 tosses? has been provided alongside types of Consider 3 coins having probability of obtaining head in a single trial as 1/4,1/2,3/4 respectively.a player select one of these three coins at random .if the player tosses the selected coin 5 times independently.then what is the probability of obtaining 2 tails in 5 tosses? theory, EduRev gives you an
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