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?
Let A be the event that the student passes English examination and B be the event that the student passes Hindi examination .
ThenP(A∩B)=0.5P(¯¯¯¯A∩¯¯¯¯B)=0.1andP(A)=0.75NowP(¯¯¯¯A∩¯¯¯¯B)=0.1⇒1−P(A∪B)=0.1⇒P(A∪B)=0.9We know thatP(A∪B)=P(A)+P(B)−P(A∩B)∴0.9=0.75+P(B)−0.5⇒0.9=0.25+P(B)⇒P(B)=0.9−025=0.65