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

1. In a factory which manufactures bolts, machine A, B and C manufacture respectively 25%, 35% and 40% of the bolts. Of their outputs 5, 4 and 2 percent are respectively defective bolts. A bolt is drawn at random from the product and is found to be defective. What is the probability that it is manufactured by machine B?--BT
2. 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 us actually six.BT
3. An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probability of an accident is 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver?BT
4. A card from the pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. Find the probability of lost card being
   i) diamond
   ii) spadeBT
5. A company has two plants to manufacture scooters. Plant I manufacture 70% of the scooters and plant II manufacture 30%. At plant I, 80% of the scooters are rated as of standard quality and at plant II, 90% of the scooters are rated as of standard quality. A scooter is chosen at random and is found to be of standard quality. What is the probability that it has come from plant II. BT
6. There are 3 bags each containing 5 white balls and 3 black balls. Also there are 2 bags each containing 2 white balls and 4 black balls. A white ball is drawn at random. Find the probability that this white ball is from the bag of first group. BT
7. In a competitive examination, 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 1/3 is and probability that he copies the answer is 1/6 . The probability that the answer is correct is, given that he copied it is 1/8 . Find the probability that he knows the answer to the squestion, given that he correctly answered the question. BT
8. Find the probability distribution of number of doublets in three throws of a pair of dice.
9. Let X denotes the number of hours you study during a randomly selected school day. The probability that X can take a value 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? PDT



10. The random variable X has probability distribution P(X) of the following form, where k is some number:
    



1. Find the value of K.
2. PDT

11. 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. PDT
12. Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X PDT OR BD
13. Let X denotes the sum of numbers obtained when two fair dice are rolled. Find the variance and standard deviation of X. PDT OR BD
14. In a meeting, 70% of the members favour 30% members 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). PDT
15. 15. Find the probability distribution of number of heads when three coins are tossed. Also find the mean number of heads in the above case. PDT OR BD
16. A pair of dice is thrown 4 times. If getting a doublet is considered a success. Find the probability of two successes. PDT OR BD
17. There are 5% defective items in a large bulk of items. What is probability that a sample of 10 items will not include more than one defective item. BD
18. A fair coin is tossed 10 times. Find the probability of
    a. Exactly six heads.
    b. At least six heads
    c. At most six heads. BD
19. Find the mean of binomial distribution (n=4 p=1/3 MEAN=np,VAR=npq)
20. Five dice are thrown simultaneously. If the occurrence of an even number in a single dice is considered a success. Find the probability of getting at most 3 successes. BD

 

Submitted By Mrs. E.Praveen
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