Q.14. If and are two events such that and then which of the following is correct?
(D) None of these
Q.13 Probability that A speaks truth is . A coin is tossed. A reports that a head appears. The probability that actually there was head is
Q. 12 A card from a pack of cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. Find the probability of the lost card being a diamond.
Q. 11 A manufacturer has three machine operators and The first operator produces defective items, where as the other two operators B and C produce and defective items respectively. is on the job for of the time, is on the job for of the time and is on the job for of the time. A defective item is produced, what is the probability that it was produced by ?
Q. 10 Suppose a girl throws a die. If she gets a or , she tosses a coin three times and notes the number of heads. If she gets or , she tosses a coin once and notes whether a head or tail is obtained. If she obtained exactly one head, what is the probability that she threw or with the die?
Q. 9 Two groups are competing for the position on the Board of directors of a corporation. The probabilities that the first and the second groups will win are and respectively. Further, if the first group wins, the probability of introducing a new product is and the corresponding probability is if the second group wins. Find the probability that the new product introduced was by the second group.
Q. 8 A factory has two machines and Past record shows that machine produced of the items of output and machine B produced of the items. Further, of the items produced by machine and produced by machine were defective. All the items are put into one stockpile and then one item is chosen at random from this and is found to be defective. What is the probability that it was produced by machine ?
Q. 7. An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probability of an accidents are , and respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver?
Q. 6. There are three coins. One is a two headed coin (having head on both faces), another is a biased coin that comes up heads of the time and third is an unbiased coin. One of the three coins is chosen at random and tossed, it shows heads, what is the probability that it was the two headed coin?
Q. 5. A laboratory blood test is effective in detecting a certain disease when it is in fact, present. However, the test also yields a false positive result for of the healthy person tested (i.e. if a healthy person is tested, then, with probability the test will imply he has the disease). If of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive ?
Q. 4. In answering a question on a multiple choice test, a student either knows the answer or guesses. Let be the probability that he knows the answer and be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability . What is the probability that the student knows the answer given that he answered it correctly?
Q.3 Of the students in a college, it is known that reside in hostel and are day scholars (not residing in hostel). Previous year results report that of all students who reside in hostel attain grade and of day scholars attain grade in their annual examination. At the end of the year, one student is chosen at random from the college and he has an grade, what is the probability that the student is a hostlier?
Q. 2 A bag contains red and black balls, another bag contains red and black balls. One of the two bags is selected at random and a ball is drawn frome bag which is found to be red. Find the probability that the ball is drawn from the first bag.
Q.1. An urn contains red and black balls. A ball is drawn at random, its colour is noted and is returned to the urn. Moreover, additional balls of the colour drawn are put in the urn and then a ball is drawn at random. What is the probability that the second ball is red?