let A denot the event that Hemant passes in english and B denote the event that hemant passes in hindi .
Given : P(A) = \(\frac{2}{3}\), P(B) = \(\frac{5}{9}\),P(A and B) = \(\frac{2}{5}\)
To find : Probability that he will pass in at least one of these subjects. = P(A or B)
Formula used : P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = \(\frac{2}{3}+\frac{5}{9}-\frac{2}{5}\)
P(A or B) = \(\frac{30+25-18}{45}\) = \(\frac{37}{45}\)
P(A or B) = \(\frac{37}{45}\)
The probability that he will pass in at least one of these subjects. = P(A or B) = \(\frac{37}{45}\)