problem 1: A box includes three white balls W1, W2, W3 and two red balls R1, R2, R3. We remove at arbitrary two balls in succession. Determine the probability that the first removed ball is red and the second is white?
problem 2: In a bolt factory machines A, B and C manufacture correspondingly 25%, 35% and 40% of the total. Of their output 5, 4, 2 % are defective bolts. A bolt is drawn from a day’s production and found to be defective .Determine the probability that it was manufactured by the C?
problem 3: Four persons prepare their names on the individual slips of paper and deposit the slips in a common box. Each of four draws at random a slip from the box. Find out the probability each person retrieving his own name slip?
problem 4: If two events A and B are independent show that ‘A’ and ‘B’ are as well independent.
problem 5: A and B take turn in throwing two dice, the first to throw 9 being awarded the prize. Show that if A has the first throw, their chance of winning is in the ratio of 9:8.
problem 6: ‘n’ letters to each of which corresponds to an envelope, are placed in envelops at arbitrary:
a) Determine the probability that no letter is placed in the right envelope?
b) Determine the probability which exactly all letters is placed in the right envelope?
problem 7: Consider the concurrent tossing of two fair coins. Determine the probability of two heads on any given trial?
problem 8: An urn includes 9 balls two of which are red; 3blue and 4 black. 3 balls are drawn from the urn at random that is every ball has an equivalent chance of being comprised in the three. Determine the chance that:
a) Three bales are of different coolers?
b) Two balls art of the same cooler and third of different?
c) The balls are of similar color?