12. A box contains 13 bulbs out of which 5 bulbs are defective. Three bulbs are drawn one by one from the box without replacement. Find the probability distribution of the number of defective bulbs drawn. An urn contains 5 white and 3 black balls. Three balls are drawn at random with replacement, (ii) without replacement obtain the probability distribution of black balls drawn. 14. A random variable X has the following distribution: X -1 0 1 2 P(X) does it represent a probability function? If yes, find its mean and variance. 15. A random variable X has the following probability distribution: X: 0 1 2 3 4 5 6 7 P(X) 0 K 2K 2K 3K Find k Obtain and 16. Three cards are drawn with replacement from a pack of 52 cards. Obtain the mean and variance of the distribution of number of kings obtained. 17. Two dice are thrown simultaneously and 'getting a number less than 3' is called a success. Obtain the mean and variance of the number of successes. 18. Four rotten mangoes are mixed accidentally with 20 good mangoes. obtain the probability distribution of the number of rotten mangoes in a random draw of 2 mangoes without replacement.
12. A box contains 13 bulbs out of which 5 bulbs are defective. Three bulbs are drawn one by one from the box without replacement. Find the probability distribution of the number of defective bulbs drawn. An urn contains 5 white and 3 black balls. Three balls are drawn at random with replacement, (ii) without replacement obtain the probability distribution of black balls drawn. 14. A random variable X has the following distribution: X -1 0 1 2 P(X) does it represent a probability function? If yes, find its mean and variance. 15. A random variable X has the following probability distribution: X: 0 1 2 3 4 5 6 7 P(X) 0 K 2K 2K 3K Find k Obtain and 16. Three cards are drawn with replacement from a pack of 52 cards. Obtain the mean and variance of the distribution of number of kings obtained. 17. Two dice are thrown simultaneously and 'getting a number less than 3' is called a success. Obtain the mean and variance of the number of successes. 18. Four rotten mangoes are mixed accidentally with 20 good mangoes. obtain the probability distribution of the number of rotten mangoes in a random draw of 2 mangoes without replacement.
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