Question

. Solve by simulating the problem.

You have a 5-question multiple-choice test. Each question has four choices. You don’t know any of the answers. What is the experimental probability that you will guess exactly three out of five questions correctly? Type your answer below using complete sentences

Answer 1

@wio

Answer 2

This is a binomial distribution.

Answer 3

@shamil98 This is good practice for you as well

Answer 4

n = 5
k = 3

Answer 5

And p?

Answer 6

p = 3/5 ?

Answer 7

Nope. A trial here is any multiple choice question.

Answer 8

If you randomly guess 1 of the 4 questions, what is probability of said trial winning?

Answer 9

1/4?

Answer 10

Yeah.

Answer 11

Do you think you can explain it to Jasmine?

Answer 12

If not I'll have to explain it a bit later.

Answer 13

Alright so, jasmine, we plug in n k and p into the following formula
f(k) = n! / k!(n-k)! p^k (1-p)^n-k

Answer 14

We have identified n k and p. So, what would the equation look like?

Answer 15

f(3)=5 / 3(5-3) 1/4 ^3 (1-1/4) ^5-3

Answer 16

Do you know what factorials are? 5! for example?

Answer 17

\[f(3) =\frac{ 5! }{ 3!(5-3)!} (1/4)^3 (1-1/4)^2\]

Answer 18

\[5! = 5 \times 4 \times 3 \times 2 \times 1 = 120\]

Answer 19

A factorial is basically every consecutive number up to that number for example..
\[3! = 3 \times 2 \times 1 = 6\]

Answer 20

\[f(3) = \frac{ 120 }{ 6 \times 2! } (1/4)^3 (1-1/4)^2\]