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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?
Most Upvoted Answer
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.
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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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