problem in statistics is given to the three students A, B and C whose chances of solvingit are 12 , 13 and 14 , respectively. What is the probability that the problem is solved
Question
problem in statistics is given to the three students A, B and C whose chances of solvingit are 12 , 13 and 14 , respectively. What is the probability that the problem is solved
Solution
The probability that the problem is solved can be found by considering the probability that at least one of the students solves the problem. This is equal to one minus the probability that none of the students solve the problem.
The probability that a student does not solve the problem is one minus the probability that the student does solve the problem. So, the probabilities that the students A, B, and C do not solve the problem are 1 - 1/2 = 1/2, 1 - 1/3 = 2/3, and 1 - 1/4 = 3/4, respectively.
The probability that none of the students solve the problem is the product of their individual probabilities of not solving the problem, 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.
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