Shopping with a smartphone.Each year, United Parcel Service (UPS) commissions a “Pulse of the Online Shopper” survey. The 2015 survey included a sample of 5,118 U.S. shoppers who have made at least two online purchases

every three months. The survey revealed that 41% of the shoppers used a smartphone to make a purchase. Of those who made a smartphone purchase, 38% indicated that they preferred the mobile Web site to the full Web site accessed through a computer. Assume these percentages represent actual probabilities for the population of online shoppers. What is the probability that a randomly selected online shopper uses a smartphone to make a purchase and

prefers the mobile Web site?

Step by step solution

01

Finding the probability that a random online shopper prefers the mobile Web site and uses a smart phone

Using the percentages we will calculate the actual values.

$\begin{array}{c}\text{No.ofsmartphoneusers=}\frac{\text{41×5118}}{\text{100}}\\ \text{=}\frac{\text{209838}}{\text{100}}\\ \text{=2098.38}\end{array}$

Number of people using smart phones is 2098.

localid="1651320414210" $\begin{array}{c}\text{No.ofsmartphoneuserspreferringmobilewebsite=}\frac{\text{38×2098}}{\text{100}}\\ \text{=}\frac{\text{79724}}{\text{100}}\\ \text{=797.24}\end{array}$

Number of smart phone users who prefer the mobile website is 797.

Using the numbers we will find the probability of a random online shopper using a smart phone and mobile website

P(A) = Smartphone user preferring mobile website

P(B) = Online shopper using a smart phone

localid="1651320495077" $\begin{array}{c}\text{P}\left(\text{A|B}\right)\text{=}\frac{\text{P(AÇB)}}{\text{P(B)}}\\ \text{=}\frac{\frac{\text{797}}{\text{5118}}}{\frac{\text{2098}}{\text{5118}}}\\ \text{=}\frac{\text{0.15}}{\text{0.41}}\\ \text{=0.36=36\%}\end{array}$

Therefore, the probability of a random shopper preferring mobile website and using a smart phone is 36%.

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