Let Ajay will not appear in JEE exam with probability p=27, while both Ajay and Vijay will appear in the exam with probability q=15. Then twice the probability, that Ajay will appear in the exam and Vijay will not appear is :

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Let Ajay will not appear in JEE exam with probability $p = \frac{2}{7},$ while both Ajay and Vijay will appear in the exam with probability $q = \frac{1}{5} .$ Then twice the probability, that Ajay will appear in the exam and Vijay will not appear is :

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$\frac{9}{35}$

$\frac{3}{35}$

$\frac{24}{35}$

$\frac{36}{35}$

answer is D.

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Detailed Solution

Probability that Ajay will not appear, $p = \frac{2}{7} .$ Both Ajay & Vijay will appear, $q = \frac{1}{5}$ Let probability that Vijay will appear be $' x'$
$\Rightarrow x . (1 - p) = q$ (independent events $x . (\frac{5}{7}) = \frac{1}{5} \Rightarrow x = \frac{7}{25}$
$∴$ Probability that ajay will appear and vijay will not appear
$= (1 - p) (1 - x) = \frac{5}{7} . \frac{18}{25} = \frac{18}{35}$