Select the correct answerA 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?Options1/21/43/47/12
Question
Select the correct answerA 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?Options1/21/43/47/12
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 process by finding the probability that none of the students solve the problem and subtracting that from 1.
The probability that the first student doesn't solve the problem is 1 - 1/2 = 1/2. The probability that the second student doesn't solve the problem is 1 - 1/3 = 2/3. The probability that the third student doesn't 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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