Show the workings on each.

Question 13: Assume that the chances of the patient having a heart attack are 40%. It is also assumed that a meditation and yoga course reduce the risk of heart attack by 30% and prescription of certain drug reduces its chances by 25%. At a time a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga?Question 15: An electronic assembly consists of two subsystems, say, A and B. From previous testing procedures, the following probabilities are assumed to be known: P(A fails) = 0.2 P(B fails alone) = 0.15 P(A and B fail ) = 0.15 Evaluate the following probabilities (i) P(A fails| B has failed) (ii) P(A fails alone)Question 16: Bag I contains 3 red and 4 black balls and Bag II contains 4 red and 5 black balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be red in colour. Find the probability that the transferred ball is black.Question 17: If A and B are two events such that P (A) * 0 and P(BIA) = 1, then. (A) AO B (B) BOA (C) B = Q (D) A = 0Question 19: If A and B are any two events such that P (A) + P (B) - P (A and B) = P (A), then (A) P (BIA) = 1 (B) P (A|B) = 1 (C) P (B|A) = 0 (D) P (A|B) = 0Question 12: Suppose we have four boxes. A, B, C and D containing coloured marbles as given below: Box Marble colour Red White Black A 1 6 3 B 6 2 2 C 8 1 1 D 6 4 One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from box A?, box B?, box C?Miscellaneous Solutions Question 1: A and B are two events such that P (A) # 0. Find P (BIA), if (i) A is a subset of B (ii) A n B = QQuestion 13: It is known that 10% of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles, 9 are defective? Answer(100 )( 100 Question 11: Find the probability of getting 5 exactly twice in 7 throws of a die. AnswerQuestion 9: On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing