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WBJEE · Maths · Probability

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

  1. A \(\frac{2}{3}\)
  2. B \(\frac{3}{5}\)
  3. C \(\frac{4}{5}\)
  4. D \(\frac{3}{4}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{4}{5}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} &\text { (c) Let } P(A)=\frac{1}{2}, P(B)=\frac{1}{3}\\ &\begin{aligned} P(C) &=\frac{1}{4}, P(D)=\frac{1}{5} \\ \text { Now, } P(A&\cup B \cup C \cup D) \\ &=1-P(\bar{A} \cap \bar{B} \cap \bar{C} \cap \bar{D}) \\ &=1-P(\bar{A}) P(\bar{B}) P(\bar{C}) P(\bar{D})…