Question
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(15 points) Assume we have purchases of 3 smartphones (iPhones, Samsung, and Nokia). We have broken down purchases by gender and age group. The results are below: 4. Phone Purchases Observation Gender Age Group Purchase 21-35 iPhone Female36-50 Samsung 51-65 iPhone Female 21-35 Samsung Female 36-50 iPhone 51-65 Samsung Male Male Male Male 21-35Samsung Male 51-65 Samsung Female 36-50 Female 36-50 iPhone 9 10 Female 21-35 iPhone Nokia Female 51-65 iPhone 12 13 14 15 Male 21-35 Samsung Female 36-50 Nokia Male 51-65 iPhone 16 Female 21-35 Nokia Female 36-50iPhone 51-65 iPhone 17 18 19 20 21 Male Male 21-35 Nokia Female 36-50 iPhone Female 51-65 Samsung Female21-35 Samsun 36-50 Nokia 23 24 25 Male Female 51-65 iPhone Female 21-35 iPhone 26 27 28 29 Male 36-50 iPhone 51-65 iPhone Female 21-35 iPhone Male Male 36-50 Samsung 30 Female 51-65 Nokia What is the probability that a consumer will buy a Samsung? What is the Complement of that probability? What is the probability that a Male will buy a Samsung? What is the probability that someone in the age group 51-65 will buy an iPhone? What is the probability that a female in the 36-50 age group will buy an iPhone? Given purchasers of iPhones, what is the probability they are in the 21-35 age group a. b. c. d.
Explanation / Answer
a)
P(consumer will buy a Samsung) = 9/30 =0.3
Hence, complement of the probability = 1 - 0.3 = 0.7
b)
P(male will buy a samsumg) = 5/30 = 0.1667
P(someone in age grop 51-65 will buy iPhone) = 6/30 = 0.2
c)
P(female in the 36-50 age group will buy iPhone = 4/30 = 0.1333
d)
P(purchaser in the 21-35 age group | purchasers of iPhone) = 4/15 = 0.2667