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14.Probability
easy
Let Ajay will not appear in JEE exam with probability $\mathrm{p}=\frac{2}{7}$, while both Ajay and Vijay will appear in the exam with probability $\mathrm{q}=\frac{1}{5}$. Then the probability, that Ajay will appear in the exam and Vijay will not appear is :
A
$\frac{9}{35}$
B
$\frac{18}{35}$
C
$\frac{24}{35}$
D
$\frac{3}{35}$
(JEE MAIN-2024)
Solution
$ \mathrm{P}(\overline{\mathrm{A}})=\frac{2}{7}=\mathrm{p} $
$ \mathrm{P}(\mathrm{A} \cap \mathrm{V})=\frac{1}{5}=\mathrm{q} $
$ \mathrm{P}(\mathrm{A})=\frac{5}{7} $
$ \text { Ans. } \mathrm{P}(\mathrm{A} \cap \overline{\mathrm{V}})=\frac{18}{35}$
Standard 11
Mathematics
