The probability that Ajay will not appear in | vedclass

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(B) Let $A$ be the event that Ajay appears in the exam and $V$ be the event that Vijay appears in the exam.Given: $P(\overline{A}) = \frac{2}{7}$,so $

Vedclass · Accepted Answer

$\frac{18}{35}$

Vedclass · Answer

(B) Let $A$ be the event that Ajay appears in the exam and $V$ be the event that Vijay appears in the exam.Given: $P(\overline{A}) = \frac{2}{7}$,so $P(A) = 1 - P(\overline{A}) = 1 - \frac{2}{7} = \frac{5}{7}$.Given: $P(A \cap V) = \frac{1}{5}$.We need to find the probability that Ajay appears and Vijay does not appear,which is $P(A \cap \overline{V})$.Using the property of sets,$P(A) = P(A \cap V) + P(A \cap \overline{V})$.Substituting the values: $\frac{5}{7} = \frac{1}{5} + P(A \cap \overline{V})$.$P(A \cap \overline{V}) = \frac{5}{7} - \frac{1}{5} = \frac{25 - 7}{35} = \frac{18}{35}$.

List-$I$	List-$II$
$(i) \ P(A \cap B)$	$(1) \ 0.4$
$(ii) \ P(A \cap \bar{B})$	$(2) \ 0.2$
$(iii) \ P(\bar{A} \cap B)$	$(3) \ 0.3$
$(iv) \ P(\bar{A} \cap \bar{B})$	$(4) \ 0.1$

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

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