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 x_{1} < x_{2} < x_{3} < x_{4} < x_{5} . Find the probability that x_{2} = 30.
b) A continuous random variable has the probability density function:
problem 2:
a) Find Mean & Variance for the following discrete distribution
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.