Question

You take a quiz with 6 multiple choice questions. After you​ studied, you estimated that you would have about an​ 80% chance of getting any individual question right. What are your chances of getting them all​ right? The random numbers below represent a simulation with 20 trials. Let​ 0-7 represent a correct answer and let​ 8-9 represent an incorrect answer.

1, 6   5   6   2   0   5
2, 4   7   3   1   6   6
3, 5   2   9   6   3   2
4, 8   0   1   6   0   8
5, 3   4   3   3   4   4
6, 2   9   1   7   3   0
7, 6   5   9   6   8   3
8, 8   6   4   4   2   7
9, 6   1   1   8   2   6
10, 5   3   0   3   8   6
11, 0   2   8   1   3   2
12, 6   8   6   0   0   4
13, 9   9   4   6   1   8
14, 1   7   3   2   5   1
15, 7   6   6   1   4   5
16, 3   5   3   1   4   5
17, 0   2   7   7   3   1
18, 3   6   1   6   1   0
19, 8   4   6   7   1   3
20, 5   3   5   2   0   9

Answer 1

Given that

Total no,of questions = 6

Total no.of chances or trials = 20

p = 0.8

q=0.2

The probability of getting all answers correct is

P(X=6) = C(6,6) * (0.8)⁶ * (0.2)^6-6

= 1*0.2621*1

=0.2621

Here in the given table

0.-7 is correct answer

8-9 is incorrect answer

No.of correct answers

1, 6   5   6   2   0   5----------------------- 6
2, 4   7   3   1   6   6----------------------- 6
3, 5   2   9   6   3   2----------------------- 5
4, 8   0   1   6   0   8----------------------- 4
5, 3   4   3   3   4   4----------------------- 6
6, 2   9   1   7   3   0----------------------- 5
7, 6   5   9   6   8   3----------------------- 4
8, 8   6   4   4   2   7----------------------- 5
9, 6   1   1   8   2   6----------------------- 5
10, 5   3   0   3   8   6--------------------- 5
11, 0   2   8   1   3   2--------------------- 5
12, 6   8   6   0   0   4--------------------- 5
13, 9   9   4   6   1   8--------------------- 3
14, 1   7   3   2   5   1--------------------- 6
15, 7   6   6   1   4   5--------------------- 6
16, 3   5   3   1   4   5--------------------- 6
17, 0   2   7   7   3   1--------------------- 6
18, 3   6   1   6   1   0--------------------- 6
19, 8   4   6   7   1   3--------------------- 5
20, 5   3   5   2   0   9--------------------- 5

Total - 104

Or you can also count how many 8's and 9's in the above table and just subtract from 120.

There are 16 (8's and 9's). So 120-16 = 104

The chance of getting all the answers correct = 104/120 = 0.867 = 86.7%