The probability of getting qualified in IITJEE and EAMCET by a student are respectively $\frac{1}{5}$ and…

The probability of getting qualified in IITJEE and EAMCET by a student are respectively $\frac{1}{5}$ and $\frac{3}{5}$. The probability that the student gets qualified for atleast one of these test, is
  1. $\frac{3}{25}$
  2. $\frac{8}{25}$
  3. $\frac{17}{25}$
  4. $\frac{22}{25}$

Solution

Given that $ P(A)=\frac{1}{5}, P(B)=\frac{3}{5} $ Required probability $ \begin{aligned} & =P(A) P(\bar{B})+P(\bar{A}) P(B)+P(A) P(B) \\ & =\frac{1}{5}\left(1-\frac{3}{5}\right)+\left(1-\frac{1}{5}\right) \cdot \frac{3}{5}+\frac{1}{5} \cdot \frac{3}{5} \\ & =\frac{1}{5} \cdot \frac{2}{5}+\frac{4}{5} \cdot \frac{3}{5}+\frac{3}{25} \\ & =\frac{2}{25}+\frac{12}{25}+\frac{3}{25}=\frac{17}{25} \end{aligned} $

Asked in: AP EAMCET 2002

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