Question

Among a student group 46% use Google Chrome, 20% Internet Explorer, 10% Firefox, 5% Mozilla, and the rest use Safari. What is the probability that you need to pick 7 students to find 2 students using Google Chrome? Report answer to 3 decimals.

Answer 1

Negative Binomial distribution :

The random variable X denote the trial at which the r^th success occurs, where r is a fixed integer. Then 'X' follows a negative Binomial distribution with 'r' and p:Probability of success

Probability mass function :P(X=x)

For the given problem,

Success : Student using Google Chrome ;

Among a student group 46% use Google Chrome, 20% Internet Explorer, 10% Firefox, 5% Mozilla, and the rest use Safari

p: Probability of success: Probability that a student uses Google chrome = 46/100 =0.46

q : 1-p=1-0.46 = 0.54

Trail : Picking a student

r^th Success = r^th student using Google Chrome : r=2 ; 2^nd student

X : Number of students you need to pick: Number of trails

X follows negative Binomial distribution with r=2 and p=0.46

Probability mass function :P(X=x)

Probability that you need to pick 7 students to find 2 students using Google Chrome = P(X=7)

Probability that you need to pick 7 students to find 2 students using Google Chrome = 0.058