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. Find the probability that a word processing program was included given that the selected individual was included a spreadsheet program. b) c) Are the vents "word processing program was included" and the event "selected individual was included a spreadsheet program" independent?

Answer 1

Let A = Word processing program included

      B = selected individual was included a spreadsheet program

We have,

            P(A) = 0.60               P(B) = 0.40            $P(A\cap B)=0.3$

a) Here only two events presents ( A and B)

Therefore, The sample space is

             $\Omega=\left \{ A,B \right \}$

b) Consider,

            $P(A/B)=\frac{P(A\cap B)}{P(B)}$

                              $=\frac{0.3}{0.4}$

                              $=0.75$

   Hence, Probability = 0.75

c) We know that event A and B are independent when

               $P(A\cap B)=P(A)P(B)$ Or $P(A/B)=P(A)$

But here,

                 $P(A/B)\neq P(A)$

   Therefore, A and B are not independent.

i.e. The events " word processing program was included" and " selected individual was included a spreadsheet program" are not independent.