# Theory of Expectation :: Drawing Balls, Cards, Items, Products :

No. Problems & Solutions [Click Hide/Show to display the solutions below the question]
01. Three marbles are drawn without replacement from an urn containing 8 red and 6 white marbles. If x is a random variable which denotes the total number of red marbles drawn, construct a table showing the probability distribution of x. also find E(x)

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02. A bag contains 5 white and 7 black balls. Find the expectation of a man who is allowed to draw two balls from the bag and who is to get one rupee for each black ball and two rupee for each white ball drawn

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03. An urn contains 7 white and 3 red balls. Two balls are drawn together, at random from this urn. Compute the probability that neither of them is white. Find also the probability of getting one white and one red ball. Hence compute the expected number of white balls drawn

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04. A box contain 8 items of which 2 are defective. A man selects 3 items at randam. Find the expected number of defective items he has drawn.

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05. A box contains 8 tickets 3 of the tickets carry a prize of Rs.5 each and the other 5 carry a prize of Rs.2
i) If one ticket is drawn, what is the expected value of the prize?
ii) If two tickets are drawn, what is the expected value of the game?

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06. For a lottery with only one prize worth Rs.3000 and 9999 blanks a person purchased a ticket which cost him Rs. 1. The mean of his income is ?

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07. 10,000 tickets one sold in a lottery in which there is a first prize of Rs. 5,000 two second prizes of Rs. 1,000 each and ten consolation prizes of Rs. 100 each one ticket cost Rs. 1 find the expected net gain or loss if you buy a ticket.

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08. Two cards are selected at random firm a box which contains five cards numbered 1, 1, 2, 2, and 3. let X denote the sum of numbers. Find the expected value of the sum

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No. Problems for Practice
01. If it rains, an umbrella sales man can earn Rs. 300 per day. If it is fair he can lose Rs. 60 per day. What is his expectation if the probability of rain is 0.3?

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