Question

The probability of receiving a A in Prob & Stats is 20%. Random picking students in a class. What is the probability that you have to select more than 3 students to get one student with A.

Group of answer choices

48.8%

20%

38.4%

87.2%

Answer 1

The probability of receiving a A in probability and statistics is 20%, ie. 0.20.

We are randomly picking students in a class.

We have to find the probability that we have to select more than 3 students to get one student with A.

Let, X be the number of students that we have to select randomly, to get a student with A.

Then, if X=i, it means we select i-1 students who do not have A, each with chance (1-0.2), ie. 0.8; then we get a student with A, which happens with chance 0.2.

So, the Probability Mass Function of X is

Where, i can take any integer value starting from 1.

Now, we have to find

Now, the term within bracket, is an Infinite geometric Progression, with first term 0.8^3, and the common ratio of 0.8.

So, the sum of the Infinite Geometric Progression is

So, we can say that

So, the corresponding percentage is 0.512*100, ie. 51.2%.

So, the correct answer is 51.2%, which is not in the group of answer choices.