1. Fix a Straight Line Trend equation by the method of Least Square Principle method. Assuming that the same rate of change continues what would be the predicted earnings for the year 1990?

Year 1981 1982 1983 1984 1985 1986 1987 1988

Earnings 38 40 65 72 69 60 87 95

2. A sample analysis of examination results of 500 students where made. It was found that 180 students have failed, 170 have secured a third class, 110 where placed in second class. Are these figure commensurate with the general examination result which is in ratio of 4:3:2:1 for the various categories respectively. 

3. In a survey of 200 boys, 75 were intelligent, 

40 had educated fathers. While 85 of unintelligent boys had uneducated father. Do these figures support the hypothesis that educated father have intelligent boys? 

4. A and B play 12 games of chess, of which 6 are won by A, 4 by B and 2 end in a tie. They agree to play 3 more games. Find the probability that

a) A win all the three games 

b) Two games end in a tie

c) A and B win alternatively and 

d) B wins at least one game.