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In an examination, the probability of a candidate solving a question is 1/2 Out of given 5 questions in the examination, what is the probability that the candidate was able to solve at least 2 questions?
- a)1/64
- b)3/16
- c)1/2
- d)13/16
Correct answer is option 'D'. Can you explain this answer?
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Probability of solving a question:
Given that the probability of a candidate solving a question is 1/2, we can say that the probability of not solving a question is 1/2 as well.
Probability of solving at least 2 questions:
To find the probability that the candidate was able to solve at least 2 questions out of the 5 given questions, we need to consider all possible scenarios where the candidate solves 2, 3, 4, or 5 questions.
Calculating the probability:
- Probability of solving exactly 2 questions:
5C2 * (1/2)^2 * (1/2)^3 = 10 * (1/4) * (1/8) = 10/32
- Probability of solving exactly 3 questions:
5C3 * (1/2)^3 * (1/2)^2 = 10 * (1/8) * (1/4) = 10/32
- Probability of solving exactly 4 questions:
5C4 * (1/2)^4 * (1/2)^1 = 5 * (1/16) * (1/2) = 5/32
- Probability of solving all 5 questions:
5C5 * (1/2)^5 = 1 * 1/32 = 1/32
Total probability of solving at least 2 questions:
Adding up the probabilities of solving 2, 3, 4, or 5 questions:
10/32 + 10/32 + 5/32 + 1/32 = 26/32 = 13/16
Therefore, the probability that the candidate was able to solve at least 2 questions is 13/16, which corresponds to option D.
Given that the probability of a candidate solving a question is 1/2, we can say that the probability of not solving a question is 1/2 as well.
Probability of solving at least 2 questions:
To find the probability that the candidate was able to solve at least 2 questions out of the 5 given questions, we need to consider all possible scenarios where the candidate solves 2, 3, 4, or 5 questions.
Calculating the probability:
- Probability of solving exactly 2 questions:
5C2 * (1/2)^2 * (1/2)^3 = 10 * (1/4) * (1/8) = 10/32
- Probability of solving exactly 3 questions:
5C3 * (1/2)^3 * (1/2)^2 = 10 * (1/8) * (1/4) = 10/32
- Probability of solving exactly 4 questions:
5C4 * (1/2)^4 * (1/2)^1 = 5 * (1/16) * (1/2) = 5/32
- Probability of solving all 5 questions:
5C5 * (1/2)^5 = 1 * 1/32 = 1/32
Total probability of solving at least 2 questions:
Adding up the probabilities of solving 2, 3, 4, or 5 questions:
10/32 + 10/32 + 5/32 + 1/32 = 26/32 = 13/16
Therefore, the probability that the candidate was able to solve at least 2 questions is 13/16, which corresponds to option D.
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In an examination, the probability of a candidate solving a question is 1/2 Out of given 5 questions in the examination, what is the probability that the candidate was able to solve at least 2 questions?a)1/64b)3/16c)1/2d)13/16Correct answer is option 'D'. Can you explain this answer?
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