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problem 1:

a) Five tickets are drawn at random from a bag containing 50 tickets numbered 1, 2, 3, - - -50. The tickets are arranged in ascending order of magnitude x1 < x2 < x3 < x4 < x5 . Find the probability that x2 = 30.

b) A continuous random variable has the probability density function:

1598_probability function.jpg

problem 2:

a) Find Mean & Variance for the following discrete distribution

570_mean and variance.jpg

b) Box ‘A’ contains 5 red, 3 white marbles and box ‘B’ contains 2 red, 6 white marbles. If a marble is drawn from each box, what is the probability that they are both of same colour

problem 3:

a) In a bold factory machines A, B, C manufacture 20%, 30% & 50% of the total of their output and 6%, 3% & 2% are defective. A bolt is drawn at random and found to be defective. Find the probabilities that it is manufactured from i) Machine B ii) Machine A.

b) Companies A, B, C produce 30%, 45% & 25% of the cars respectively. It is known that 2%, 3%, 2% of the cars produced from A, B, C are defective. What is the probability that a car purchased is defective?If a car purchased is found to be defective, what is the probability that it is produced by company ‘C’ ?

problem 4:

a) A, B & C in order toss a coin. The first one to toss head wins the game. What is the probability that A’ starts the game & ‘B’ wins the game.

b) A box contains ‘n’ number tickets marked 1 to n. Two tickets are drawn in succession without replacement. Determine the probability that the number on the tickets are consecutive integers.

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