math stat college question ASAP

Question

Suppose you are taking a multiple-choice quiz that you are completely unprepared for. The quiz consists of 6 questions and each question has five possible answers to choose from. Thus, the probability of guessing the correct answer for any individual question is 20%.

Explain how you would use randomly generated numbers from 1 to 5 to model you taking the quiz and guessing on every question?

Answer 1

Well, the random number represents the option selected.

1=A 2=B 3=C 4=D 5=E

SIX (6) of these random numbers shall be generated and these 6 random

integers between 1 and 5 inclusive are the coding for the answers on the quiz

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Here is a table for the binomial probabilities if you are interested...

K is the # of CORRECT answers out of 6

k 6-k (6 choose k) 0.2^k (0.8)^(6-k) Probability

0 6 1 1 0.262144 0.262144

1 5 6 0.2 0.32768 0.393216

2 4 15 0.04 0.4096 0.24576

3 3 20 0.008 0.512 0.08192

4 2 15 0.0016 0.64 0.01536

5 1 6 0.00032 0 .8 0.001536

6 0 1 0.000064 1 0.000064

So the probability of getting 3 out of 6 is just over 8%

the probability of getting none of them is just over 26%

and the probability of getting only 1 correct is 39%.

The probability of getting 2 correct is just over 24.5%

this makes sense because the EXPECTED value is 6 * 0.2 = 1.2

so you are most likely to 1 correct out of 6, with 0 or 2 correct

answers next most likely