Question

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.

Answer 1

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) =  \(\frac{37}{45}\)