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The probabilites of solving a problem by three students A, B, C independently are 1/2 , 1/3 , 1/4 . The probability that the problem will be solved is
- a)1/60
- b)3/4
- c)48/60
- d)57/60
Correct answer is option 'B'. Can you explain this answer?
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The probabilites of solving a problem by three students A, B, C indepe...
Given probabilities of solving the problem by three students A, B, C independently are:
P(A) = 1/3
P(B) = 1/4
P(C) = 1/5
To find the probability that the problem will be solved, we can use the formula:
P(A or B or C) = P(A) + P(B) + P(C) - P(A and B) - P(A and C) - P(B and C) + P(A and B and C)
Now, we need to find the values of P(A and B), P(A and C), P(B and C), and P(A and B and C).
P(A and B) = P(A) × P(B) = (1/3) × (1/4) = 1/12
P(A and C) = P(A) × P(C) = (1/3) × (1/5) = 1/15
P(B and C) = P(B) × P(C) = (1/4) × (1/5) = 1/20
P(A and B and C) = P(A) × P(B) × P(C) = (1/3) × (1/4) × (1/5) = 1/60
Substituting the values in the formula, we get:
P(A or B or C) = 1/3 + 1/4 + 1/5 - 1/12 - 1/15 - 1/20 + 1/60
P(A or B or C) = 36/60
Therefore, the probability that the problem will be solved is 36/60, which simplifies to 3/5, or option B.
P(A) = 1/3
P(B) = 1/4
P(C) = 1/5
To find the probability that the problem will be solved, we can use the formula:
P(A or B or C) = P(A) + P(B) + P(C) - P(A and B) - P(A and C) - P(B and C) + P(A and B and C)
Now, we need to find the values of P(A and B), P(A and C), P(B and C), and P(A and B and C).
P(A and B) = P(A) × P(B) = (1/3) × (1/4) = 1/12
P(A and C) = P(A) × P(C) = (1/3) × (1/5) = 1/15
P(B and C) = P(B) × P(C) = (1/4) × (1/5) = 1/20
P(A and B and C) = P(A) × P(B) × P(C) = (1/3) × (1/4) × (1/5) = 1/60
Substituting the values in the formula, we get:
P(A or B or C) = 1/3 + 1/4 + 1/5 - 1/12 - 1/15 - 1/20 + 1/60
P(A or B or C) = 36/60
Therefore, the probability that the problem will be solved is 36/60, which simplifies to 3/5, or option B.
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The probabilites of solving a problem by three students A, B, C independently are 1/2 , 1/3 , 1/4 . The probability that the problem will be solved isa)1/60b)3/4c)48/60d)57/60Correct answer is option 'B'. Can you explain this answer?
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