Apple market researchers are interested in purchasing behaviors of people toward

Question

Apple market researchers are interested in purchasing behaviors of people toward electronics, specifically iPods, iPads, and iPhones. Let’s call the event A1 : a person selected at random owns an iPod, A2 : a person selected a t random owns an iPad, and A3 : a person selected at random owns an iPhone. Out of a sample of 1000 people, they found that P(A1) = 0.6, P(A2) = 0.5, and P(A3) = 0.4. Assume that the decision to purchase any of them is independent from the others.

For each of the events below, sketch them in a venn diagram and find their probability.

a. ) A1 A2; A2 A3; A1 A3.

b. ) A1 A2; A2 A3; A1 A3.

c. ) A1 A2 A3.

d. ) A1 A2 A3.

e. ) C : a person selected at random owns no electronics of the three

f. ) D : a person selected at random owns all three electronics, given that they own at least one.

g. ) Are the events A1 and A2 disjoint? What about A1 and A3? What about A2 and A3?

Explanation / Answer

a)P(A1 A2)= P(A1)*P(A2) =0.6*0.5=0.3

P(A2 A3) =P(A2)*P(A3) =0.5*0.4 =0.2

P(A1 A3)=P(A1)*P(A3) =0.6*0.4=0.24

b) P(A1 A2) =P(A1)+P(A2)-P(A1 A2) = 0.6+0.5 -0.3= 0.8

P(A2 A3) =P(A2)+P(A3)-P(A2 A3) = 0.5+0.4 -0.2= 0.7

P(A3 A1) =P(A1)+P(A3)-P(A1 A3) = 0.6+0.4 -0.24= 0.76

c)

P(A1 A2 A3) =P(A1)*P(A2)*P(A3) =0.6*0.5*0.4 =0.12

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.