Engineering
Mathematics
Addition Theorem on Probability
Basic Definitions Related to Probability
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, then the probability of passing the Hindi examination is
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Solution
P(E ⋂ H) = 0.5 ; P(Ec ⋂ Hc) = 0.1
1 – P(E ⋃ H) = 0.1
∴ P(E ⋃ H) = 0.9
P(E) + P(H) – P(E ⋂ H) = 0.9
⇒ 0.75 + p – 0.5 = 0.9
⇒ p = 1.40 – 0.75 = 0.65.