The probability that the problem will be solved by three persons are 1/2, 1/3 and 1/6. Find the probability that the problem is solved ?a)11/18b)13/18c)15/18d)17/18Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Given information:
- The problem will be solved by three persons.
- The probability that the problem will be solved by the first person is 1/2.
- The probability that the problem will be solved by the second person is 1/3.
- The probability that the problem will be solved by the third person is 1/6.

To find: The probability that the problem is solved.

Solution:
We can solve this problem using the concept of complementary events. The complementary event of the problem being solved is the event of the problem not being solved. So, we can find the probability of the problem not being solved and subtract it from 1 to get the probability of the problem being solved.

Let's calculate the probability of the problem not being solved by any of the three persons:

Probability that the problem is not solved by the first person = 1 - 1/2 = 1/2
Probability that the problem is not solved by the second person = 1 - 1/3 = 2/3
Probability that the problem is not solved by the third person = 1 - 1/6 = 5/6

To find the probability that the problem is not solved by any of the three persons, we multiply the probabilities of the individual events:

P(problem not solved) = (1/2) * (2/3) * (5/6) = 5/18

Now, we can find the probability that the problem is solved by subtracting the probability of the problem not being solved from 1:

P(problem solved) = 1 - P(problem not solved) = 1 - 5/18 = 13/18

Therefore, the probability that the problem is solved is 13/18, which corresponds to option 'B'.

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