Question

Visors to your website are asked to answer a single survey question before they get access to the content on the page. Among all of the users, there are two categories 1. Random Clicker (RC) 2. Truthful Clicker (TC) There are two possible answers to the survey: yes and no. Random clickers would click either one with equal probability. You are also giving the information that the expected fraction of random clickers is 0.3. After a trial period, you get the following survey results. 65% said Yes and 35% said No. How many people people who are truthful clickers answered yes?

Answer 1

Answer:

The percentage of visitors who are truthful clickers and answered yes is 15%.

Step-by-step explanation:

Denote the events as follows:

Y = a visitor clicked Yes.

N = a visitor clicked No.

R = a visitor is a random clicker.

T = a visitor is a truthful clicker.

Given:

$P(Y) = 0.65\\P(N) = 0.35\\P(Y|R) = 0.50 = P (N|R)\\P (R) = 0.30\\P (T) = 1 - P (R) = 1- 0.30 =0.70$

The law of total probability states that:

$P(A)=P(A|B)P(B)+P(A|C)P(C)$

The probability of Y can be computed using the law above as$P(Y)=P(Y|R)P(R)+P(Y|T)P(T)$

Compute the value of P (Y|T) as follows:

$P(Y)=P(Y\cap R)+P(Y\cap T)\\P(Y)=P(Y|R)P(R)+P(Y|T)P(T)\\0.65=(0.50\times0.30)+P(Y\cap T)\\P(Y\cap T)=0.65-0.15\\P(Y\cap T)=0.15$

Percentage = 0.15 × 100 = 15%.

Thus, the percentage of visitors who are truthful clickers and answered yes is 15%.