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Q.

The probability of getting qualified in IIT & JEE and EAMCET by a student are respectively $\frac{1}{5} and \frac{3}{5}$ . The probability that the student gets qualified for at least one of these test, is

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a

$\frac{22}{25}$

b

$\frac{3}{25}$

c

$\frac{17}{25}$

d

$\frac{8}{25}$

answer is C.

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Detailed Solution

Given
$P (A) = \frac{1}{5}, P (B) = \frac{3}{5} ∴ Requried probability \begin{array}{l} = P (A) P (\bar{B}) + P (\bar{A}) P (B) + P (A) P (B) \\ = \frac{1}{5} (1 - \frac{3}{5}) + (1 - \frac{1}{5}) \cdot \frac{3}{5} + \frac{1}{5} \cdot \frac{3}{5} \\ = \frac{1}{5} \cdot \frac{2}{5} + \frac{4}{5} \cdot \frac{3}{5} + \frac{3}{25} \\ = \frac{2}{25} + \frac{12}{25} + \frac{3}{25} = \frac{17}{25} \end{array}$

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