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This section contains 2 paragraphs. Based upon one of paragraph 2 multiple choice questions and based on the other paragraphs 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct
A box has 10 coins. Five have heads on both sides. Three have tails on both sides; two are fair. A coin is chosen at random and tossed.
Probability that the coin is fair given that head has appeared is
- a)5/6
- b)1/6
- c)3/8
- d)5/8
Correct answer is option 'B'. Can you explain this answer?
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This section contains 2 paragraphs. Based upon one of paragraph 2 mult...
Probability of selecting a fair coin:
- In the given box, there are a total of 10 coins.
- Out of these, 5 coins have heads on both sides, 3 coins have tails on both sides, and 2 coins are fair.
- The probability of choosing a fair coin from the box is given by the ratio of the number of fair coins to the total number of coins.
- Therefore, the probability of selecting a fair coin is 2/10, which simplifies to 1/5.
Probability of getting a head when a fair coin is tossed:
- Since we have selected a fair coin, we know that it has heads on one side and tails on the other side.
- When we toss this fair coin, there are only two possible outcomes: heads or tails.
- Since the coin is fair, the probability of getting a head is equal to the probability of getting a tail, which is 1/2.
Probability of selecting a fair coin given that a head has appeared:
- We are given that a head has appeared after tossing the randomly selected coin.
- Now we need to find the probability that the coin is fair, given this information.
- This probability can be found using Bayes' theorem, which states that the probability of an event A given that event B has occurred is equal to the probability of event B given that event A has occurred, multiplied by the probability of event A, divided by the probability of event B.
- In this case, event A is selecting a fair coin, and event B is getting a head.
- Using the values we calculated earlier, the probability of selecting a fair coin given that a head has appeared is (1/2) * (1/5) / (1/2), which simplifies to 1/5.
Therefore, the correct answer is option B) 1/6.
- In the given box, there are a total of 10 coins.
- Out of these, 5 coins have heads on both sides, 3 coins have tails on both sides, and 2 coins are fair.
- The probability of choosing a fair coin from the box is given by the ratio of the number of fair coins to the total number of coins.
- Therefore, the probability of selecting a fair coin is 2/10, which simplifies to 1/5.
Probability of getting a head when a fair coin is tossed:
- Since we have selected a fair coin, we know that it has heads on one side and tails on the other side.
- When we toss this fair coin, there are only two possible outcomes: heads or tails.
- Since the coin is fair, the probability of getting a head is equal to the probability of getting a tail, which is 1/2.
Probability of selecting a fair coin given that a head has appeared:
- We are given that a head has appeared after tossing the randomly selected coin.
- Now we need to find the probability that the coin is fair, given this information.
- This probability can be found using Bayes' theorem, which states that the probability of an event A given that event B has occurred is equal to the probability of event B given that event A has occurred, multiplied by the probability of event A, divided by the probability of event B.
- In this case, event A is selecting a fair coin, and event B is getting a head.
- Using the values we calculated earlier, the probability of selecting a fair coin given that a head has appeared is (1/2) * (1/5) / (1/2), which simplifies to 1/5.
Therefore, the correct answer is option B) 1/6.
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This section contains 2 paragraphs. Based upon one of paragraph 2 multiple choice questions and based on the other paragraphs 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correctA box has 10 coins. Five have heads on both sides. Three have tails on both sides; two are fair. A coin is chosen at random and tossed.Probability that the coin is fair given that head has appeared isa)5/6b)1/6c)3/8d)5/8Correct answer is option 'B'. Can you explain this answer?
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This section contains 2 paragraphs. Based upon one of paragraph 2 multiple choice questions and based on the other paragraphs 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correctA box has 10 coins. Five have heads on both sides. Three have tails on both sides; two are fair. A coin is chosen at random and tossed.Probability that the coin is fair given that head has appeared isa)5/6b)1/6c)3/8d)5/8Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about This section contains 2 paragraphs. Based upon one of paragraph 2 multiple choice questions and based on the other paragraphs 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correctA box has 10 coins. Five have heads on both sides. Three have tails on both sides; two are fair. A coin is chosen at random and tossed.Probability that the coin is fair given that head has appeared isa)5/6b)1/6c)3/8d)5/8Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for This section contains 2 paragraphs. Based upon one of paragraph 2 multiple choice questions and based on the other paragraphs 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correctA box has 10 coins. Five have heads on both sides. Three have tails on both sides; two are fair. A coin is chosen at random and tossed.Probability that the coin is fair given that head has appeared isa)5/6b)1/6c)3/8d)5/8Correct answer is option 'B'. Can you explain this answer?.
This section contains 2 paragraphs. Based upon one of paragraph 2 multiple choice questions and based on the other paragraphs 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correctA box has 10 coins. Five have heads on both sides. Three have tails on both sides; two are fair. A coin is chosen at random and tossed.Probability that the coin is fair given that head has appeared isa)5/6b)1/6c)3/8d)5/8Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about This section contains 2 paragraphs. Based upon one of paragraph 2 multiple choice questions and based on the other paragraphs 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correctA box has 10 coins. Five have heads on both sides. Three have tails on both sides; two are fair. A coin is chosen at random and tossed.Probability that the coin is fair given that head has appeared isa)5/6b)1/6c)3/8d)5/8Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for This section contains 2 paragraphs. Based upon one of paragraph 2 multiple choice questions and based on the other paragraphs 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correctA box has 10 coins. Five have heads on both sides. Three have tails on both sides; two are fair. A coin is chosen at random and tossed.Probability that the coin is fair given that head has appeared isa)5/6b)1/6c)3/8d)5/8Correct answer is option 'B'. Can you explain this answer?.
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