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Three candidates solve a question. Odds in favour of the correct answer are 5:2,4:3 and 3:4 respectively for the three candidates. What is the probability that at least two of them solve the question correctly?
- a)209/343
- b)134/343
- c)149/343
- d)60/343
Correct answer is option 'A'. Can you explain this answer?
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Probability of at least two candidates solving the question correctly:
Calculating the probability:
- Let's calculate the probability of each candidate solving the question correctly:
- Candidate 1: Probability = 5/(5+2) = 5/7
- Candidate 2: Probability = 4/(4+3) = 4/7
- Candidate 3: Probability = 3/(3+4) = 3/7
Probability of at least two candidates solving the question:
- To find the probability that at least two candidates solve the question correctly, we need to calculate the probabilities of different combinations:
- Probability that exactly two candidates solve the question:
- P(2 candidates) = P(Candidate 1 and Candidate 2) + P(Candidate 1 and Candidate 3) + P(Candidate 2 and Candidate 3)
- P(2 candidates) = (5/7 * 4/7) + (5/7 * 3/7) + (4/7 * 3/7)
- P(2 candidates) = 20/49 + 15/49 + 12/49 = 47/49
- Probability that all three candidates solve the question:
- P(all 3 candidates) = P(Candidate 1 and Candidate 2 and Candidate 3)
- P(all 3 candidates) = 5/7 * 4/7 * 3/7 = 60/343
Final probability:
- Probability of at least two candidates solving the question = P(2 candidates) + P(all 3 candidates)
- Probability = 47/49 + 60/343 = 209/343
Therefore, the correct answer is option A) 209/343.
Calculating the probability:
- Let's calculate the probability of each candidate solving the question correctly:
- Candidate 1: Probability = 5/(5+2) = 5/7
- Candidate 2: Probability = 4/(4+3) = 4/7
- Candidate 3: Probability = 3/(3+4) = 3/7
Probability of at least two candidates solving the question:
- To find the probability that at least two candidates solve the question correctly, we need to calculate the probabilities of different combinations:
- Probability that exactly two candidates solve the question:
- P(2 candidates) = P(Candidate 1 and Candidate 2) + P(Candidate 1 and Candidate 3) + P(Candidate 2 and Candidate 3)
- P(2 candidates) = (5/7 * 4/7) + (5/7 * 3/7) + (4/7 * 3/7)
- P(2 candidates) = 20/49 + 15/49 + 12/49 = 47/49
- Probability that all three candidates solve the question:
- P(all 3 candidates) = P(Candidate 1 and Candidate 2 and Candidate 3)
- P(all 3 candidates) = 5/7 * 4/7 * 3/7 = 60/343
Final probability:
- Probability of at least two candidates solving the question = P(2 candidates) + P(all 3 candidates)
- Probability = 47/49 + 60/343 = 209/343
Therefore, the correct answer is option A) 209/343.
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