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A problem in probability was given to three CA students A, B and C whose chances of solving it as 1/3, 1/5 and 1/2 respectively. What is the probability that the problem would be solved? (a)4/5 (b)7/8 (c)8/15 (d)11/15?
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A problem in probability was given to three CA students A, B and C who...
Solution:
Given, the chances of solving the problem by A, B, and C are 1/3, 1/5, and 1/2 respectively.
Let P(A), P(B), and P(C) be the probabilities of solving the problem by A, B, and C respectively.
Therefore, P(A) = 1/3, P(B) = 1/5, P(C) = 1/2.
The probability that the problem would be solved is given by the formula:
P(solved) = P(A) + P(B) + P(C) - P(A and B) - P(B and C) - P(A and C) + P(A and B and C)
where P(A and B) represents the probability that both A and B solve the problem, and so on.
We need to find P(solved).
Calculating the probabilities of intersection:
P(A and B) = P(A) × P(B) = (1/3) × (1/5) = 1/15
P(B and C) = P(B) × P(C) = (1/5) × (1/2) = 1/10
P(A and C) = P(A) × P(C) = (1/3) × (1/2) = 1/6
P(A and B and C) = P(A) × P(B) × P(C) = (1/3) × (1/5) × (1/2) = 1/30
Substituting the values in the formula:
P(solved) = (1/3) + (1/5) + (1/2) - (1/15) - (1/10) - (1/6) + (1/30)
P(solved) = 11/15
Therefore, the probability that the problem would be solved is 11/15.
Hence, the correct option is (d) 11/15.
Given, the chances of solving the problem by A, B, and C are 1/3, 1/5, and 1/2 respectively.
Let P(A), P(B), and P(C) be the probabilities of solving the problem by A, B, and C respectively.
Therefore, P(A) = 1/3, P(B) = 1/5, P(C) = 1/2.
The probability that the problem would be solved is given by the formula:
P(solved) = P(A) + P(B) + P(C) - P(A and B) - P(B and C) - P(A and C) + P(A and B and C)
where P(A and B) represents the probability that both A and B solve the problem, and so on.
We need to find P(solved).
Calculating the probabilities of intersection:
P(A and B) = P(A) × P(B) = (1/3) × (1/5) = 1/15
P(B and C) = P(B) × P(C) = (1/5) × (1/2) = 1/10
P(A and C) = P(A) × P(C) = (1/3) × (1/2) = 1/6
P(A and B and C) = P(A) × P(B) × P(C) = (1/3) × (1/5) × (1/2) = 1/30
Substituting the values in the formula:
P(solved) = (1/3) + (1/5) + (1/2) - (1/15) - (1/10) - (1/6) + (1/30)
P(solved) = 11/15
Therefore, the probability that the problem would be solved is 11/15.
Hence, the correct option is (d) 11/15.
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A problem in probability was given to three CA students A, B and C whose chances of solving it as 1/3, 1/5 and 1/2 respectively. What is the probability that the problem would be solved? (a)4/5 (b)7/8 (c)8/15 (d)11/15?
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