Answer Happy

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Question 1 Suppose you flipped a coin 3 times. What is the probability of getting- (i) Two heads and one tail. (ii) Three tails. Question 2 Suppose your neighbour has two children. You know that between two children, he has a son named Joy. What is the probability that Joy's sibling is a brother? Question 3 A school is offering two extracurricular classes, one in Playing Chess and the other in Painting. These classes are open to all of the 350 students in the school. Suppose there are 58 students in the Playing Chess class, 44 in the Painting class, and 22 who are in both classes. If a student is randomly chosen, what is the probability that this student is not enrolled in any one of these classes? Question 4 A person has taken a job to build a project. The probabilities of completion of the job on time with and without rain are 0.40 and 0.92 respectively. If the probability that it will rain is 0.44, then determine the probability that the project will be completed on time. Question 5 Bag A contains six red and seven black balls and Bag B contains nine red and six black balls. One ball is transferred from Bag A to Bag B and then a ball is drawn from Bag B. The ball so drawn is found to be black in colour. Find the probability that the transferred ball was red. 1 Question 6 A recent survey showed that 14% of men would likely develop prostate cancer at some point in their lives. A man with prostate cancer has 93% chance of a positive test result from a medical screening exam. A man without prostate cancer has a 9% chance of getting a false-positive test result. What is the probability that a man has cancer given he has a positive test result? Question 7 Suppose a game in which, on any play, a player has a 25% chance of winning Tk. 40 and 75% chance of losing Tk. 15. What is the expected gain or loss of the player in the end? Question 8 Assume that the chances of a patient suffering from high blood pressure is 60%. It is also assumed that a course of meditation reduces the risk of high blood pressure by 45% and the prescription of certain drugs reduces its chances by 55%. 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 does not suffer from high blood pressure. Find the probability that the patient chose a course of meditation?