A problem is given to three students whose chances of solving it are 1/2, 1/3and ¼ respectively. What is the probability that the problem will be solved?Options1/43/47/121/2
Question
A problem is given to three students whose chances of solving it are 1/2, 1/3and ¼ respectively. What is the probability that the problem will be solved?Options1/43/47/121/2
Solution
To solve this problem, we need to use the formula for the probability of the union of three events, which is P(A U B U C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C).
However, in this case, we can simplify the problem by finding the probability that none of the students solve the problem and subtracting that from 1.
The probability that the first student does not solve the problem is 1 - 1/2 = 1/2.
The probability that the second student does not solve the problem is 1 - 1/3 = 2/3.
The probability that the third student does not solve the problem is 1 - 1/4 = 3/4.
The probability that none of the students solve the problem is the product of these probabilities, which is (1/2) * (2/3) * (3/4) = 1/4.
Therefore, the probability that at least one of the students solves the problem is 1 - 1/4 = 3/4.
So, the correct answer is 3/4.
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