CBSE Guess > Papers > Important Questions > Class XII > 2010 > Maths > Mathematics By Mr Vasu Raj

CBSE CLASS XII

Q. 21. Let X denote the number of hours you study during a randomly selected school day. The probability that X can take the values x, has the following form, where k is some unknown constant.
 

(a) Find the value of k.
(b) What is the probability that you study at least two hours ? Exactly two hours? At most two hours?

Ans. a) k = 0.15  
b)  0.75 ,  0.3  ,  0.55

Q. 22. Find the variance of the number obtained on a throw of an unbiased die.

Ans. 35/12

Q. 23. Two cards are drawn simultaneously (or successively without replacement) from a well shuffled pack of 52 cards. Find the mean, variance and standard deviation of the number of kings.

Ans. 34/221,6800/4884(0.1392), 0.37

Q. 24. 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.

Q. 25. A coin is biased so that the head is 3 times as likely to occur as tail. If the coin is tossed twice, find the probability distribution of number of tails.

Q. 26 . A random variable X has the following probability distribution.

Determine (i) k (ii) P(X < 3) (iii) P(X > 6) (iv) P(0 < X < 3)

Q. 27. Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find E(X).

Ans. 14/3

Q.28. A class has 15 students whose ages are 14, 17, 15, 14, 21, 17, 19, 20, 16, 18, 20, 17, 16, 19 and 20 years. One student is selected in such a manner that each has the same chance of being chosen and the age X of the selected student is recorded. What is the probability distribution of the random variable X? Find mean, variance and standard deviation of X.

Ans. 17.53, 4.78, 2.19

Q. 29. If a fair coin is tossed 10 times, find the probability of  (i) exactly six heads (ii) at least six heads (iii) at most six heads

Ans. 105/512, 193/512, 53/64

Q. 30.There are 5% defective items in a large bulk of items. What is the probability  that a sample of 10 items will include not more than one defective item?

Ans.

Q. 31. 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.

Ans.
 
Miscellaneous

Q . 31 A and B throw a die alternatively till one of them gets a ‘6’ and wins the game. Find their respective probabilities of winning, if A starts first.

Ans. 6/11, 5/1.

Q. 32 . 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. 

Ans. 20/21

Paper By Mr Vasu Raj
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