Question

A problem in mathematics is given to 4 students whose chances of solving individually are \(\frac{1}{2}, \frac{1}{3}, \frac{1}{4}\) and \(\frac{1}{5}\). The probability that the problem will be solved at least by one student is
(A) \(\frac{2}{3}\)
(B) \(\frac{3}{5}\)
(C) \(\frac{4}{5}\)
(D) \(\frac{3}{4}\)

Answer 1

Ans: (C)
Hint \(: P(A \cup B \cup C \cup D)=1-P\left(A^{C} \cap B^{C} \cap C^{C} \cap D^{C}\right)\)
\(=1-P\left(A^{C}\right) \cdot P\left(B^{C}\right) \cdot P\left(C^{C}\right) \cdot P\left(D^{C}\right)\)
\(=1-\frac{1}{2} \times \frac{2}{\not 2} \times \frac{\not p}{4} \times \frac{\not 4}{5}\)
\(=1-\frac{1}{5}=\frac{4}{5}\)

Answer 2

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Answer 3

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