Page 1 CBSE TEST PAPER-03 CLASS - XII MATHEMATICS (Probability) Topic: - Probability 1. Find the probability distribution of number of doublets in three throws of a pair of dice. [4] 2. Let X denote the no of hours you study during a randomly selectee school day. The probability that X can take the values x, has the following form where K is some unknown constant ( ) 0.1 if x = 0 if x = 1, or 2 p K (5 - x) if x = 3 or 4 0, otherwise kx x ? ? ? ? = = ? ? ? ? (a) Find the value of K (b) What is the probability that you study at least two hours. Exactly two hours? At most 2 hr. [4] 3. Find the variance of the number obtained on a throw of an unbiased die. [4] 4. Two cards are drawn simultaneously (or successively without replacement) for a well shuffled of 52 cards. Find the mean, variance and standard deviation of the number of kings. [6] 5. 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. [6] 6. In a meeting 70% of the members favour and 30% oppose a certain proposal. A member is selected at random and we take x = 0 if he opposed and x = 1 if he is in favour. Find E (x) and var (x). [6] 7. A and B throw a die alternatively till one of them gets a ‘6’ and win the game. Find their respective probabilities of winning if A starts first. [6] 8. Find the mean of the Binomial distribution B 1 4, 3 ? ? ? ? ? ? [6] 9. If a leap year is selected at random, what is the chance that it will contain 53 Tuesdays? [4] 10. Bag I contain 3 red and 4 black balls and bag II contain 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 fund to be red in colour. Find the probability that the transferee ball is black. [6]Read More

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