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A problem in probability was given to three CA students A, B and C whose chances of solving it are 1/3, 1/5 and 1/2 respectively. What is the probability that the problem would be solved?
- a)4/15
- b)7/8
- c)8/15
- d)11/15
Correct answer is option 'D'. Can you explain this answer?
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A problem in probability was given to three CA students A, B and C who...
Solution:
Given probabilities 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.
Then, the probability of the problem being solved is given by the formula:
P(A) + P(B) + P(C) - P(A and B) - P(B and C) - P(C and A) + P(A and B and C)
Where P(A and B) represents the probability of solving the problem by both A and B, P(B and C) represents the probability of solving the problem by both B and C, and so on.
Now, let's calculate each of these probabilities:
P(A) = 1/3
P(B) = 1/5
P(C) = 1/2
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(C and A) = P(C) × P(A) = 1/2 × 1/3 = 1/6
P(A and B and C) = P(A) × P(B) × P(C) = 1/3 × 1/5 × 1/2 = 1/30
Substituting these values in the formula, we get:
P(solving the problem) = P(A) + P(B) + P(C) - P(A and B) - P(B and C) - P(C and A) + P(A and B and C)
= 1/3 + 1/5 + 1/2 - 1/15 - 1/10 - 1/6 + 1/30
= 11/30
Therefore, the probability of solving the problem is 11/15.
Hence, the correct answer is option D.
Given probabilities 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.
Then, the probability of the problem being solved is given by the formula:
P(A) + P(B) + P(C) - P(A and B) - P(B and C) - P(C and A) + P(A and B and C)
Where P(A and B) represents the probability of solving the problem by both A and B, P(B and C) represents the probability of solving the problem by both B and C, and so on.
Now, let's calculate each of these probabilities:
P(A) = 1/3
P(B) = 1/5
P(C) = 1/2
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(C and A) = P(C) × P(A) = 1/2 × 1/3 = 1/6
P(A and B and C) = P(A) × P(B) × P(C) = 1/3 × 1/5 × 1/2 = 1/30
Substituting these values in the formula, we get:
P(solving the problem) = P(A) + P(B) + P(C) - P(A and B) - P(B and C) - P(C and A) + P(A and B and C)
= 1/3 + 1/5 + 1/2 - 1/15 - 1/10 - 1/6 + 1/30
= 11/30
Therefore, the probability of solving the problem is 11/15.
Hence, the correct answer is option D.
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A problem in probability was given to three CA students A, B and C whose chances of solving it are 1/3, 1/5 and 1/2 respectively. What is the probability that the problem would be solved?a)4/15b)7/8c)8/15d)11/15Correct answer is option 'D'. Can you explain this answer?
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