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

21. An unbiased dice is thrown three times. Getting 3 or 5 is considered as success. Find the probability of at least two successes. BD
22. An urn contains seven white, 5 black and 3 red balls. Two balls are drawn at random.
    Find the probability that :
    i. Both the balls are red.
    ii. One ball is red and other is black.
    iii. One ball is white.
23. 3 cards are drawn at random from a pack of well shuffled 52 cards. Find the probability that :
    i. All the three cards are of same suit.
    ii. One is a king; the other is a queen and third is a jack.
24. There are two bags I and II. Bag I contains 3 white and 2 red balls, bag II contains2 white and 4 red balls. A ball is transferred from bag I to bag II (without seeing its colour) and then ball is drawn from bag II. Find the probability of getting a red ball.
25. Bag I contains 3 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. BT
26. A problem in mathematics is given to three students whose chances of solving it are 1/2, 1/3, 1/4 . What is the probability in the following cases
    i) the problem is solved
    ii) Only one of them solves it correctly.
27. Five dice are thrown simultaneously . If the occurrence of an even number is considered as a “ success” , find the probability of at most 3 successes BD
28. 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 tested then with probability 0.005, the test will imply that 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 the test result is positive ? BT
29. A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability distribution of number of succeses. PDT
30. If E and F are independent events prove that E and F’ are independent.
31. If a machine is correctly set up, it produces 90% acceptable items. If it is incorrectly set up, it produces only 40% acceptable items. Past experience shows that 80% of the set ups are correctly done. If after a certain set up, the machine produces 2 acceptable items, find the probability that the machine is correctly set up. BT-NOTE THE 2.SEE TEXT BOOK EXAMPLE SUM
32. Let x denote a number of collages where you will apply after your results and P( X = x ) denote your probability of getting admission in x number of collage it is given that
    (i) Find the value of K
    (ii) What is the probability that you will get admission in exactly two collages
    (iii) Find the mean & variance of probability distributions.

k is positive constant         

33. If A and B are independent events then prove that A’ and B’ are also independent events
34. From a lot of 30 bulbs which include 6 defectives, a sample of 4 bulbs is drawn at random with replacement. Find the probability distribution of the number of defective bulbs.
35. In a test, and examinee 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. BT
36. Two cards are drawn successively with replacement from a well-shuffled pack of 52 cards .find the probability distribution of the number of aces .find its mean and standard deviation.
37. In shuffling a pack of 52 playing cards, four are accidentally dropped .find chance that missing cards should be one from each suit.
38. If P(A) = 0.2, P(B) = 0.3 and P (A U B ) = 0.4, where a & b are two events associated with a random experiment. Find P (A ∩ B) and P(A / B)
39. A bag contains 3 white, 4 red and 5 black balls. Two balls are drawn one after the other without replacement. Find the probability that of the two drawn balls, one is white and the other is black.
40. Two dice are throw together. What is the probability that the sum of the number on the two faces is divisible by 3 or 4?

 

Submitted By Mrs. E.Praveen
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