Question

The probability that a student will pass the final examination in both

English and Hindi is 0.5 and the probability of passing neither is 0.1. If the

probability of passing the English examination is 0.75. What is the

probability of passing the Hindi examination ?

Answer 1

Let E be event that student passed in English examination

$\therefore$P(E) = 0.75

Let H be event that student passed in Hindi examination

$\therefore$P(H) = ?

Also, $P(E\cap H)=0.5$ and

P(\overline{E} \cap \overline{H}) =0.1

$\therefore P(\overline{E}\cap \overline{H})=1-P(E\cup H)$

$\Rightarrow P(E\cup H)=1-0.1=0.9$

Now by addition theorem,

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

0.9= 0.7 + P(H)-0.5

P(H) = 0.90-0.25 = 0.65