Question

Apple Inc. decided to conduct a survey to find out how many customers have iPhones and ipads. Out of 10,000 costumers, 8,000 have iPhones, and 6,000 have iPads. 5,000 customers are reported to have both iPhones and iPads. Suppose a customer is selected randomly:

a) What is the probability that the customer is an iPhone owner? (.8)

b) What is the probability that the customer has both, iPhone and iPad? (.5)

c) What is the probability that the customer has iPad, given that he has an iPhone? (0.625)

d) Are the events has an iPhone and has iPad independent? Explain

Answer 1

A : Event of Iphone

B : Event of Ipad

n(s) = total number of costumers in sample space = 10000

Cosider

n( A ) = number of costumers having iPhones = 8000

n( B ) = number of costumers having iPad = 6000

a ) probability that the customer is an iPhone owner

Anser for a part

Probability that the customer is an iPhone owner = 0.8

b }

Final answer for b

probability that the customer has both, iPhone and iPad = 0.5

c}

Here we formula of the conditional probability

So we get

P ( B | A ) = 0.625

Final answer for c

probability that the customer has iPad, given that he has an iPhone = 0.625

d)

No the events has an iPhone and has iPad independent

Beacuse for the independence we require the condtion

P ( B | A) = P ( B)   then two event are said to be Independent

Here above contion is not satisfied

n( B ) = number of costumers having iPads = 6000

P ( B ) = probability that the customer is an iPad owner

and

P(B|A ) = 0.625

Hence

Hence events has an iPhone and has iPad are not Independent