Page 1 CBSE TEST PAPER-02 CLASS - XII MATHEMATICS (Probability) Topic: Probability 1. Given three identical boxes I, II and III each containing two coins. In box-I both coins are gold coins, in box-II, both are silver coins and in the box-III, there is one gold and one silver coin. A person chooses a box at random and takes out a coin. If the coin is of gold, what is the probability that the other coin in the box is also of gold. [6] 2. Suppose that the reliability of a HIV test is specified as follows of people having HIV, 90% of the test detect the disease but 10% go undetected of people free of HIV, 99% of the test are Judged HIV â€“ tive but 1% are diagnosed as showing HIV +tive. From a large population of which only 0.1% have HIV, one person is selected at random, given the HIV test, and the pathologist reports him/her is HIV +tive what is the probability that the person actually has HIV. [6] 3. In a factory which manufactures bolts, machines. A, B and C manufacture respectively 25%, 35% and 40% of the bolts. Of their output 5,4 and 2 percent are respectively defective bolts. A bolt is drown at random from the product and is found to be defective. What is the probability that it is manufactured by the machine B. [6] 4. A doctor is to visit a patient. From the past experience, it is known that the probabilities that he will come by train, bus, scooter or by other mean of transport are respectively 3 1 1 2 , , and . 10 5 10 5 The probabilities that he will be late are 1 1 1 , , and 4 3 12 if he comes by train, bus and scooter respectively, but he comes by other means of transport, that he will not the late. When he arrives he is late. What is the probability that he comes by train. [6] 5. A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. Find the probability that it is actually a six. [6] Page 2 CBSE TEST PAPER-02 CLASS - XII MATHEMATICS (Probability) Topic: Probability 1. Given three identical boxes I, II and III each containing two coins. In box-I both coins are gold coins, in box-II, both are silver coins and in the box-III, there is one gold and one silver coin. A person chooses a box at random and takes out a coin. If the coin is of gold, what is the probability that the other coin in the box is also of gold. [6] 2. Suppose that the reliability of a HIV test is specified as follows of people having HIV, 90% of the test detect the disease but 10% go undetected of people free of HIV, 99% of the test are Judged HIV â€“ tive but 1% are diagnosed as showing HIV +tive. From a large population of which only 0.1% have HIV, one person is selected at random, given the HIV test, and the pathologist reports him/her is HIV +tive what is the probability that the person actually has HIV. [6] 3. In a factory which manufactures bolts, machines. A, B and C manufacture respectively 25%, 35% and 40% of the bolts. Of their output 5,4 and 2 percent are respectively defective bolts. A bolt is drown at random from the product and is found to be defective. What is the probability that it is manufactured by the machine B. [6] 4. A doctor is to visit a patient. From the past experience, it is known that the probabilities that he will come by train, bus, scooter or by other mean of transport are respectively 3 1 1 2 , , and . 10 5 10 5 The probabilities that he will be late are 1 1 1 , , and 4 3 12 if he comes by train, bus and scooter respectively, but he comes by other means of transport, that he will not the late. When he arrives he is late. What is the probability that he comes by train. [6] 5. A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. Find the probability that it is actually a six. [6] 6. In answering a question on a multiple choice test a student either knows the answer or guesses Let 3 4 be the probability that he knows the answer and ¼ be the probability he guesses. Assuming that a student who guesses at the answer will be correct with probability 1 4 . What is the probability that the student knows the answer given that he answered it correctly. [6] 7. A laboratory blood test is 99% effective in detecting a certain disease when it is in fact, present. However, the test also yields a false positive result for 0.5% of the healthy person tested (i. e if a healthy person is test then with probability 0.005 the test will imply he has the disease) If 0.1 percent of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive. [6] 8. An insurance company insured 2000 scooter drivers, 4000, car drivers and 6000 truck drivers. The probability of accidents is 0.01, 0.03 and 0.15 respectively. One of the insured persons meet with an accident what is the probability that he is scooter driver. [6] 9. A card from a pack of 52 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. [6] 10. Suppose a girl throws a die. If she gets a 5 or 6, she tosses a coin three times and notes the number of heads. If she gets 1, 2, 3, 4, she tosses a coin once and notes whether a head or tail is obtained. If she obtained exactly one had, what is the probability that she threw 1, 2, 3 or 4 with the die? [6]Read More

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