The probability that Hemant passes in English is (2/3) and the probability that he passes in Hindi is (5/9). If the probability of his passing both the subjects is (2/5), find the probability that he will pass in at least one of these subjects.

Engineering

Mathematics

Conditional Probability

Question

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E: passes in English

H: passes in Hindi

P(E) = 2/3 P(H) = 5/9

P(E⋂H) = 2/5

P(EUH) = ?

P(EUH) = P(E) + P(H) – P(E⋂H)

$= \frac{2}{3} + \frac{5}{9} - \frac{2}{5}$

$= \frac{30 + 25 - 18}{45}$

$P (E \cup H) = \frac{37}{45}$

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