If the probability for A to fail in an examination is 0.2 and that for B is 0.3 , then the probability that either A or B fail is

Step-by-step solution

Let P(A) be the probability that A fails and P(B) be the probability that B fails. Given P(A) = 0.2 and P(B) = 0.3 . Since the events of A and B failing are independent, the probability that both fail is P(A B) = P(A) P(B) = 0.2 0.3 = 0.06 . The probability that either A or B fails is given by the addition theorem of probability: P(A B) = P(A) + P(B) - P(A B) . Substituting the values, we get P(A B) = 0.2 + 0.3 - 0.06 = 0.5 - 0.06 = 0.44 . Answer: 0.44