CHAPTER 3 



Elementary Probability 



Several relatively small populations of data have been studied be- 

 cause it is not feasible to use large groups of data in the classroom. 

 Quite commonly, populations actually involve a very large number 

 of numerical measurements; so large, in fact, that their number can 

 be considered as infinite without doing appreciable violence to the 

 subsequent analyses. Obviously, no more than a portion (sample) 

 of the measurements in an infinite population can be obtained for 

 study. Sampling theory requires certain probability considerations 

 and some definite assumptions regarding the distribution of the meas- 

 urements in the population (as noted in section 2.8). Hence it is 

 appropriate to consider some of the more basic and widely used fre- 

 quency distributions before attacking the problems of sampling. 

 That is done in this and the following chapter. 



Probability is involved whenever the occurrence, or non-occurrence, 

 of any anticipated event is dependent to some degree upon chance. 

 An "event" can be any sort of occurrence or non-occurrence which 

 has been specified in advance. In the classroom, red and green 

 marbles might be placed in a sack, thoroughly mixed, and one drawn 

 out without looking into the sack. The drawing of a green marble 

 could be considered as the event E in this instance. Likewise, if a 

 bridge deck is thoroughly shuffled and one card drawn at random 

 from it, the appearance of the ace of spades then might be the event 

 E. 



Another wide application of probability in everyday life lies in 

 the determination of the premiums for life insurance policies and 

 annuities. If a man aged 35 years purchases an annuity which will 

 pay him $100 per month starting at age 60 if he is alive, there are 

 three major matters to be considered: (a) interest on the money 

 involved, (6) the probabilities that the man will live to receive each 

 successive payment, and (c) operating expenses and a fair profit for 



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