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. I fthe probability of passing the English examination is 0.75, What is the probability of passing he HINDI examination?

Answer 1

Let A be the event that the student passes English examination and B be the event that the student passes Hindi examination .
$\text{Then}P(A\cap B)=0.5P(\overline{A}\cap \overline{B})=0.1andP\left(A\right)=0.75\text{Now}P(\overline{A}\cap \overline{B})=0.1\Rightarrow 1-P(A\cup B)=0.1\Rightarrow P(A\cup B)=0.9\text{We know that}P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)\therefore 0.9=0.75+P\left(B\right)-0.5\Rightarrow 0.9=0.25+P\left(B\right)\Rightarrow P\left(B\right)=0.9-025=0.65$