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?
The probability of passing the Hindi examination is 0.65.
Explanation
This question tests the understanding of probability operations involving union and intersection of events. The key concept used is the relationship P(E ∪ H) = P(E) + P(H) - P(E ∩ H), along with the complement rule P(E' ∩ H') = 1 - P(E ∪ H). Students need to recognize that 'passing neither' corresponds to the complement of the union of passing either subject.
Solution Steps
Step 1: Let E be the event of passing English and H be the event of passing Hindi. Given: P(E ∩ H) = 0.5, P(E' ∩ H') = 0.1, and P(E) = 0.75.
Step 2: Using the complement rule: P(E' ∩ H') = 1 - P(E ∪ H). Therefore, P(E ∪ H) = 1 - 0.1 = 0.9.
Step 3: Using the addition formula: P(E ∪ H) = P(E) + P(H) - P(E ∩ H). Substituting values: 0.9 = 0.75 + P(H) - 0.5.
Step 4: Solving for P(H): P(H) = 0.9 - 0.75 + 0.5 = 0.65.