Many internet apps, services and advertising rely on people clicking on links. A

Question

Many internet apps, services and advertising rely on people clicking on links. Assume a basic scenario where the probability of someone clicking a link is 0.019. You and three of your friends, Mo, Chen and Sam have seen the link.

Q1 What is the probability that none of you have clicked on the link?

Q2 What is the probability that you and Chen clicked the link?

Q3 What is the probability that at least two of your group of friends have clicked the link?

A company is working on its marketing campaign. Pre-tests show that it is reasonable to assume the same probability that someone who sees the link will click on it of 0.019. This link is relevant to a broad audience, so the company contracts with an internet platform that promises to show the link to 10,000 people.

Q4 What is the probability that more than 215 will click on the link?

The company is also interested in how its customers feel about the links it provides. Based on a recent survey, the company believes 25% of its 20,000 customers appreciate the links the company provides.

Q5 If the company sends a certain link to 5,000 of its customers, what is the probability that fewer than 1200 of those customers will appreciate the link?

Explanation / Answer

#1.
Probability = (1 - 0.019)^4 = 0.9261

#2.
Probability = 0.019^2 * (1 - 0.019)^2 = 0.000347

#3.
As per binomial distribution,
P(X=r) = nCr * p^r * (1-p)^(n-r)

P(X >=2) = 1 - P(X <2)
P(X < 2) = P(X = 0) + P(X = 1)

P(X = 0) = (1 - 0.019)^4 = 0.9261
P(X=1) = 4C1 * 0.019^1 * (1-0.019)^(4-1) = 0.0717

P(X >=2) = 1 - 0.9979 = 0.0021

#4.
mean = 0.019*10000 = 190
sd = sqrt(0.019*(1-0.019)*10000) = 13.6525

P(X > 215)
= P(z > (215 - 190)/13.6525)
= P(z > 1.8312)
= 0.0335

required probability = 0.0335

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