Let Ajay will not appear in JEE exam with probability while both Ajay and Vijay will appear in the exam with probability Then the probability that Ajay will appear in the exam and Vijay will not appear is

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Solution

Q.
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 the probability that Ajay will appear in the exam and Vijay will not appear is [2024]

1 $\frac{9}{35}$

2 $\frac{3}{35}$

3 $\frac{24}{35}$

4 $\frac{18}{35}$

Ans.
(4)

We have, $P (Not Ajay) = P = \frac{2}{7} \Rightarrow P (Ajay) = P = \frac{5}{7}$

$P (Ajay \cap Vijay) = q = \frac{1}{5}$

$∴$ $P (Ajay \cap not Vijay) = \bar{p} - q = \frac{5}{7} - \frac{1}{5} = \frac{18}{35}$

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