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A problem in statistics is given to three students A, B and C whose chances of solving it independently are 1/2, 1/3,  and 1/4 respectively. The probability that the problem will be solved is
  • a)
    1/12
  • b)
    11/12
  • c)
    1/2
  • d)
    3/4
Correct answer is option 'D'. Can you explain this answer?
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Problem Analysis

To solve this problem, we need to find the probability that the problem will be solved by at least one of the three students. We are given the individual probabilities of each student solving the problem independently. Let's solve this step-by-step.

Solution

Step 1: Finding the probability that none of the students solve the problem

The probability that student A does not solve the problem is 1 - 1/2 = 1/2.
Similarly, the probability that student B does not solve the problem is 1 - 1/3 = 2/3.
And the probability that student C does not solve the problem is 1 - 1/4 = 3/4.

Since the events of each student not solving the problem are independent, we can multiply these probabilities together to find the probability that none of the students solve the problem:
P(None of the students solve the problem) = (1/2) * (2/3) * (3/4) = 1/4

Step 2: Finding the probability that at least one of the students solves the problem

The probability that at least one of the students solves the problem is equal to 1 minus the probability that none of the students solve the problem:
P(At least one student solves the problem) = 1 - P(None of the students solve the problem)
P(At least one student solves the problem) = 1 - 1/4 = 3/4

Therefore, the probability that the problem will be solved is 3/4, which corresponds to option 'D' as the correct answer.
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