1) In a bolt factory, machine A, B and C manufacture respectively 25%, 35% and 40% of the total bolts. Of their output 5, 4 and 2 percent are respectively defective bolts. A bolt is drawn at random from the product. If the bolt drawn is found to be defective, what is the probability that is manufactured by the machine B? 28/69
2) Three urns contain 6 red, 4 Black: 4 red, 6 black; and 5red , five black balls respectively. One of the urns is selected at random and a ball is drawn from it. If the ball drawn is red, find the probability that it is drawn from the first urn. 2/5
3) A company has two plants to manufacture scooters. Plant I manufactures 70% of the scooters and Plant II manufacturers 30%. At plant I, 80% of the scooters are rated as of a standard quality and at Plant II, 90% of the scooters are rated as of standard quality. A scooter is choosen at random and is found to be standard quality. What is the probability that it has come from Plant II? 27/83
4) An Insurance company insured 2000 scooter drivers , 4000 car drivers and 6000 truck drivers . The probability of an accident involving a scooter driver, car driver and a truck driver are 0.01, 0.03 and 0.15 respectively. One of the insured person meets with an accident. What is the probability that he is a scooter driver? 1/52
5) Urn A contains 2 white, one Black and 3 red balls , urn B contains 3 white, 2 black and 4 red balls and urn C contains 4 white, 3 black balls and 2 Red balls . One urn is chosen at random and 2 balls are drawn at random from the urn. If the chosen happen to be red and black, what is the probability that both balls come from urn B ? 20/53
6) There are 3 bags, each containing 5 white balls and 3 black balls. Also there are two bags, each containing two White balls and 4 black balls . A white ball is drawn at random. Find the probability that this white ball is from a bag of the first group. 45/61
7) 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 hearts. Find the probability of the missing card to be a heart. 11/50
8) Suppose a girl throws a die. If she gets a 5 or 6, she tosses a coin 3 times and notes the number of heads. if she gets a 1, 2, 3 or 4, 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 a 1, 2, 3 or 4 with the die? 8/11
9) Given 3 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 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 a gold ? 2/3
10) A bag I contains three 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. 16/31
11) Suppose that 5% of men and 0.25% of women have grey hair. A grey haired person is selected at random. What is the probability of this person being male ? Assume that there are equal number of males and females. 20/21
12) A bag contains 4 balls. Two balls are drawn at random and are found to be white. What is the probability that all balls are white ? 3/5
13) A bag contains 3 red and 7 black balls. Two balls are selected at random one-by- one without replacement. If the second selected ball happens to be red, what is the probability that the first selected ball is also red ? 2/9
14) Suppose that 6% of the people with blood group O are left handed and 10% of those who other blood groups are left handed. 30% of the people have blood group O. If a left handed person is selected at random, what is the probability that he/she will have blood group O ? 9/44
15) 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. 3/8
16) In a test, an examine either guesses or copies or knows the answer to a multiple choice question with 4 choices. The probability that he makes a guess is 1/3 and the probability that he copies the answer is 1/6. The probability that his answer is correct, given that he copied it, is 1/8. Find the probability that he knew the answer to the question, given that he correctly answered it. 24/29
17) A letter is known to have come from TATANAGAR or CALCUTTA . On the envelop just two consecutive letters TA are visible. What is the probability that the letter has come from
a) CALCUTTA. 4/11
b) TATANAGAR. 7/11
18) A doctor is to visit a patient. From the past experience, it is known that the probability that he will come by train, bus, scooter or by other means of transport are respectively 3/10, 1/5,1/10 and 2/5. The probability that he will be late 1/4,1/3 and 1/12, if he comes by train, bus and scooter respectively, but if he comes by other means of transport, then he will not be late, When he arrives, he is late. What is the probability that he comes by train . 1/2
19) Let d₁, d₂, d₃ be three mutually exclusive diseases . Let S={s₁, s₂, s₃,..., s₆} be the set of observable symptoms of these diseases . For example s₁ is the shortness of breath , s₂ is loss of weight, s₃ is fatigue . Suppose a random sample of 10000 patients contains 3200 patients with disease d₁, 3500 with disease d₂ and 3300 with disease d₃. Also, 3100 patients with disease d₁, 3300 with disease d₂ and 3000 with disease d₃ show the symptom S. Knowing that the patient has symptoms S, the doctor wishes to determine the patient 's illness. On the basis of this information, what should the doctor conclude ? P(E₃/A)< P(E₁/A)< P(E₂/A) i.e., P(E₂/A) is largest. This, the doctor should conclude that the patient is most likely to have disease d₂
20) Suppose that the realibilty of 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% the test are judged HIV-ve but 1% are diagnosed as showing HIV+ve. From the 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 as HIV+ve. What is the probability that the person actually has HIV ? 90/1089
21) Suppose you have two coins which appear identical in your pocket. You know that one is fair and one is 2-headed. If you take one out, toss it and get a head, what is the probably that it was a fair coin ? 1/3
22) Three bags contains a number of red and white balls are as follows:
Bag I :3 red balls; Bag II : 2 red balls and 1 white ball; bag III : 3 white balls.
The probably that bag i will be chosen and a ball is selected from it is i/6, i= 1, 2, 3. If a white ball is selected, what is the probability that it come from
a) bag I. 2/11
b) bag II. 9/11
c) bag III.
23) A shopkeeper sells three types of seeds A₁, A₂ and A₃. They are sold as a mixture where the proportion are 4:4:2 respectively. The germination rates of the three types of seeds are 45%, 60%, and 35%. calculate the probability
a) that it will not germinate given that seed is of type A₃. 0.65
b) of a randomly chosen seed to germinate. 0.49
c) that it is of type A₂ given that a randomly chosen seed does not germinate. 16/51
RAW - A
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