The probability that Hemant passes in English is (2/3), and the probab

1.	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» 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) = \(\frac{37}{45}\)

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»

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) = \(\frac{37}{45}\)

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