Question

Q3: Suppose that of all individuals buying a certain personal computer, 60% include a word processing program in their purchase, 40% include a spreadsheet program, and 30% include both types of programs. We are interested in knowing the inclusion of the programs.

a) Write out the sample space for the problem.

b) Find the probability that a word processing program was included given that the selected individual was included a spreadsheet program.

c) Are the vents “word processing program was included” and the event “selected individual was included a spreadsheet program” independent?

Answer 1

GIVEN:

Let W be the event where individuals include a word processing program in their purchase.

Let S be the event where individuals include a spreadsheet program in their purchase.

Probability that individuals include a word processing program in their purchase

Probability that individuals include a spreadsheet program in their purchase

Probability that individuals include both word processing and spreadsheet program in their purchase

(a) SAMPLE SPACE:

The following table is the table of probabilities:

	Include Spreadsheet	Does not include Spreadsheet	TOTAL
Include Word processing	0.30	(0.60-0.30) = 0.30	0.60
Does not Include Word processing	(0.40-0.30) = 0.10	(0.40-0.10)= 0.30	(1-0.60) =0.40
TOTAL	0.40	(1-0.40) = 0.60	1.00

The sample space for the problem is given by,

(b) PROBABILITY THAT WORD PROCESSING PROGRAM WAS INCLUDED GIVEN THAT SELECTED INDIVIDUAL INCLUDED A SPREADSHEET PROGRAM :

The probability that a word processing program was included given that the selected individual was included a spreadsheet program is given by,

Probability that individuals include both word processing and spreadsheet program in their purchase

Probability that individuals include a spreadsheet program in their purchase

Thus the probability that a word processing program was included given that the selected individual was included a spreadsheet program is given by,

  

  

Thus the probability that a word processing program was included given that the selected individual was included a spreadsheet program is .

(c) WHETHER THE EVENTS "WORD PROCESSING PROGRAM WAS INCLUDED" AND "SPREADSHEET PROGRAM WAS INCLUDED" ARE INDEPENDENT:

The two events "WORD PROCESSING PROGRAM WAS INCLUDED" (W) and "SPREADSHEET PROGRAM WAS INCLUDED" (S) are said to be independent is it satisfies the following condition:

Probability that individuals include both word processing and spreadsheet program in their purchase

  

Since , we conclude that the two events "WORD PROCESSING PROGRAM WAS INCLUDED" (W) and "SPREADSHEET PROGRAM WAS INCLUDED" (S) are dependent.