$\begin{array}{1 1}(A)\;0.65\\(B)\;0.75\\(C)\;0.85\\(D)\;0.35\end{array} $

- $P(A\cup B)=P(A)+P(B)-P(A\cap B)$
- $P(A)+P(A')=1$

Step 1:

Let H denote Hindi,E denote English

Given :

$P(H\cap E)=0.5$

P(passing neither)=$P(H'\cap E')=P(H \cup E)'=0.1$

$\therefore P(H \cup E)=1-P(H\cup E)'$

$\Rightarrow 1-0.1$

$\Rightarrow 0.9$

Step 2:

Also given $P(E)=0.75$

$\therefore P(H\cup E)=P(H)+P(E)-P(H\cap E)$

$0.9=P(H)+0.75-0.5$

$\;\;\;\;\;\;=P(H)+0.25$

$0.9-0.25=P(H)$

$\Rightarrow P(H)=0.65$

$\therefore$ Probability of passing Hindi exam is 0.65

Hence (A) is the correct answer.

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