CBSE Guess > Papers > Important Questions > Class XII > 2011 > Maths > Maths By Mrs. E.Praveen

CBSE CLASS XII

Probability

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Bt - BayesTheorem;
Pdt -Probability Distribution
Bd - Binomial Distribution

81. A pair of dice is thrown twice. If the random variable X is defined as the number of doublets, find the probability distribution of X. Also find the mean and variance for above distribution.
82. Suppose that the reliability of HIV test is specified as follows: Of the people having HIV, 90% of the test detect the disease but 10% go undetected. Of people free of HIV, 90% of the test are judged HIV –ive but 1% are diagnosed as showing HIV +ive. 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 as HIV +ive. What is the probability that the person actually has HIV? BT
83. A letter is known to have come either from LONDON or CLIFTON. On the envelope just two consecutive letters ON are visible. What is the probability that the letter has come from (i) LONDON (ii) CLIFTON. BT
84. A and B throw a pair of die turn by turn. The first to throw 10 is awarded a prize. If B starts the game. What is the probability that A is getting prize.
85. A manufacturer has three machine operators A,B and C. The first operator A produces 1% defective items, where as the other two operators B and C produce 5% and 7% defective items respect$ively. A is on the job for 50% of the item, B is on the job for 30% of the time and C is on the job for the remaining time .If a defective item is produced, what is the probability that it was produced by A? BT
86. In an examination, 20 questions of true-false type are asked. Suppose a student tosses a fair coin to determine his answer to each question. If the coin falls heads, he answers ‘true’, if it falls tails, he answers ‘false’. Find the probability that he answers at least 12 questions correctly.
87. A die is thrown again and again until three sixes are obtained. Find the probability of obtaining the third six in the sixth throw of the die.
88. The probability that a certain person will buy a shirt is 0.2, the probability that he will buy a the probability that he will buy both a shirt and a trouser. Find also the probability that he will trouser is 0.3 and the probability that he will buy a shirt given that he buys a trouser is 0.4. Find the probability that he buys a trouser given that he buys a shirt.
89. Three persons A, B, throw a die in succession till one gets a ‘six’ and wins the game. Find their respective probabilities of winning, if A begins.
90. In a test, an examinee either guesses or copies or knows the answer to a multiple choice question with four 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 knows the answer to the question, given that he correctly answered it. BT
91. Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that
    (i) both balls are red
    (ii) one of them is black and the other is red.
92. In a hurdle race, a race player has to cross hurdles. The probability that he will be each hurdle is 4/5. What is the probability that he will knock down fewer than 2 hurdles? BD
93. A bag X contains 2 white and 3 red balls and a bag Y contains 4 white and 5 red balls.Oneball is drawn at random from one of the bag and is found to be red. Find the probability that it was drawn from bag Y. BT
94. 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. BT
95. In a binomial distribution, the sum of mean and variance of 5 trials is 3.75.Find the distribution.
96. Suppose that 80% of people are right handed. What is the probability that at most 6 of a random sample of 10 people are right handed? BD
97. Two cards are drawn successively with replacement from a well-shuffled of 52 cards. Find the P.D, mean and variance for the number of kings. BD
98. Two cards are drawn without replacement from a well-shuffled of 52 cards. Find the P.D, mean and variance for the number of aces. BD
99. An urn contains 5 red and 3 black balls. Find the P.D of the number of blue balls in a draw of 2 balls with replacement.
100. An insurance company insured 2000 scooters, 3000 car and 4000 track drivers. The probabilities of their meeting with an accident are 0.04, 0.06 and 0.15 respectively. If one of person meets with an accident then find the probability that he is a car driver.
101. A bag contains 6 red and 7 blue balls and another bag contains 5 red and 4 blue balls. A ball is drawn from the first bag and without noticing its color is put in the second bag. A ball is then drawn from the second bag. Find the probability that the ball is drawn is blue in color.
102. A speaks truth in 60% of the cases and B in 70% of the cases. In what percentages of cases they are likely to (i) contradict each other (ii)agree with each other, in stating same fact?
103. A problem in mathematics is given to three students who’s chancing of solving it are 1/2, 1/3 and 1/4 respectively. What is the probability that the problem will be solved?
104. A husband and wife appear in an interview for two vacancies in the same post. The probability of husband’s selection is 1/5 and that of wife’s selection is 1/3. What is the probability that
     (i) both are selected
     (ii) only one is selected
     (iii) none is selected
     (iv) at least one selected?
105. In a group, there are 3 women and 4 men. Three persons are selected at random from this group. Find the probability that 2 women and 1 man or 1 woman and 2 men are selected.
106. Two cards are drawn at random, without replacement from a pack of 52 cards, find the probability that both the cards will be red.
107. The probability that a student selected at random will pass in mathematics 2/3 and the probability that he/she passes in mathematics and c.s is 1/5. What is the probability that he/she will pass in c.s if it is known that he/she has passed in mathematics?
108. Given P(A) = 1/2, P(B) = 1/3 and P(A U B) = 2/3. Are the events A and B independent?

 

Submitted By Mrs. E.Praveen
Email Id : [email protected]