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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 exam

20. The probability that a student will pass the final examination in both English and Hindi is  \small 0.5 and the probability of passing neither is \small 0.1. If the probability of passing the English examination is  \small 0.75, what is the probability of passing the Hindi examination?

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Let A be the event that the student passes English examination and B be the event that the students pass Hindi examination.

Given, 

P(A)=0.75, P(A  \cap B) = 0.5, P(A' \cap B') =0.1

We know,

P(A' \cap B') = 1 - P(A \cup B)

\implies P(A \cup B) = 1 - 0.1 = 0.9

Also,

P(A \cup B) = P(A)+ P(B) - P(A \cap B) 

\implies P(B) = 0.9 - 0.75 + 0.5 = 0.65

Hence,the probability of passing the Hindi examination is 0.65

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