A test consists of 10 multiple choice questions with five choices for each question. As an experiment, you GUESS on each and every answer without even reading the questions. What is the probability of getting exactly 6 questions correct on this test?

a. 0.6%

b. 0.00001%

c. 0.0064%

d. 0.0002%

A.

Step-by-step explanation:

Firstly, we should know that this problem is a Bernoulli trial problem.

We shall be using the equation of the trial later in the question.

We know that there are 5 options per questions, this mean that there are a total of 10 * 5 = 50 options.

Now, we also know that there are 10 correct options and 40 incorrect ones.

The probability of selecting a correct option is 10/50 = 0.2

The probability of selecting an incorrect option is 40/50 = 0.8

We know that since he is selecting exactly 6 correct answers, there has to be 4 incorrect ones, since he's attempting 10 questions.

Applying this parameters in the equation yields the following:

(10C6) * (0.2) ^6 * (0.8) ^4 = 210 * 0.000064 * 0.4096 = 0.005505024

This is approximately equal to 0.006

The answers in the options are in percentage. Hence we convert the decimal to percentage.

6/1000 * 100% = 0.6%