The probability that a student passes Physics test is 2/3 and the probability that he passes both Physics test and English test is 11/15 . The probability that he passes at least one test is 4/5 . What is the probability that he passes English test?

Step-by-step solution

Let P be the event of passing the Physics test and E be the event of passing the English test. Given: P(P) = 2 3 P(P E) = 11 15 P(P E) = 4 5 Using the addition theorem of probability: P(P E) = P(P) + P(E) - P(P E) Substituting the given values: 4 5 = 2 3 + P(E) - 11 15 P(E) = 4 5 - 2 3 + 11 15 Taking the LCM of the denominators, which is 15 : P(E) = 12 - 10 + 11 15 P(E) = 13 15 Answer: 13/15