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

What exactly is giving you problems?

Answer 2

the whole thing

Answer 3

Well, what would the chance be to get a single question right, if we ignore the other 4?

Answer 4

1/5

Answer 5

The question has 4 choices, not 5.

Answer 6

sorry 1/4

Answer 7

Right, so what would the chance be to get 3 questions right if we ignore the other 2?

Answer 8

3/4

Answer 9

Well, that seems a bit strange, doesn't it? Because that would mean answering 3 questions is easier than answering one question. surely that can't be right?

Answer 10

What you did here is 1/4 + 1/4 + 1/4. Try multiplying instead.

Answer 11

I did 1/4*3 and I got 3/4

Answer 12

True, but what I meant is \[\left( \frac{ 1 }{ 4 } \right)^3 = \frac{ 1 }{ 4}*\frac{ 1 }{ 4 }*\frac{ 1 }{4 }\]

which is definitely not 3/4

Otherwise, the chance of answering 5 questions correctly would be 5/4, which would be impossible.

Answer 13

1/64

Answer 14

yes, that's right. Although that is still only part of our answer, since that would be the chance of getting 3 or more questions correctly, since we still ignored the other 2 questions.

So we also need to take into account the two questions which must be incorrect.

Answer 15

You know the chance of answering a question incorrectly (just one question on its own)?

Answer 16

yes if there is only 1 question that you answer and you get it wrong its 0/1

Answer 17

I mean the chance of getting the question wrong. If the chance of getting it right is 1/4 then what would the chance of getting it wrong be?

Answer 18

1/4

Answer 19

If a question has 4 options, and only 1 of them is right, how many wrong answers are there to a question?

Answer 20

3 would be wrong

Answer 21

True

Answer 22

So, if we use the same method as for the 3 right questions, if we want to know the chance of getting 2 wrong questions, we multiply 2 wrong questions with each other, so

\[\left( \frac{ 3 }{ 4 } \right)^2 = \frac{ 3 }{ 4 }*\frac{ 3 }{ 4 }\]

Answer 23

And whatever the result of that is, we multiply the outcome with \(\frac{ 1 }{ 64 }\) for the final answer.

Answer 24

I got 9/256 for the answer

Answer 25

Really?

Answer 26

From 3/4*3/4 or the final answer?

Answer 27

Becausr \[\frac{ 3 }{ 4 }*\frac{ 3 }{ 4 }=\frac{ 3*3 }{ 4*4 }=\frac{ 9 }{ 16 }\]

and

\[\frac{ 9 }{ 16 } *\frac{ 1 }{ 64 }=\frac{ 9*1 }{ 16*64 }=\frac{ 9 }{ 1024}\]

Answer 28

Somehow your answer is 4 times larger.

Answer 29

I did \[3/4^{2} * 1/16\]

Answer 30

and I got 9/256

Answer 31

how?

Answer 32

how what?

Answer 33

How did you calculate \( 3/4^{2} * 1/16 \)

Answer 34

(should be \( (3/4)^2 \) btw, because the 3 is also squared, but even then the outcome is not what i would expect.

Answer 35

I would still get 9/256

Answer 36

Can you do it step by step? or do oyu put it in a calculator or something?

Answer 37

i put it in the calculator

Answer 38

What exactly did you type into the calculator?

Answer 39

\[(3/4_{2}) * 1/16\]

Answer 40

That's weird because \[\left( 3/4^2 \right)*1/16 = 3/256\]

and \[\left( \frac{ 3 }{4 } \right)^2*1/16 = 9/1024\]

Neither is 9/256

Answer 41

i keep getting 9/256

Answer 42

oh lol

Answer 43

it's 1/64 not 1/16

Answer 44

How did i not see that sooner

Answer 45

So nothing is wrong with your calculator, it's just you used 1/16 instead of 1/64 which is exactly 4 times larger.

Answer 46

so i took \[\left( 3/4 \right)^{2} * \left( 1/64 \right)\] i got 0.008789063

Answer 47

Yeah, that's a decimal approximation, it's actually 0.0087890625 (9/1024)

But it's close enough.

Answer 48

oh ok

Answer 49

You'd probably get the same value if you type 9/1024 in your calculator, maybe it only goes 10 digits. Mine goes about a 1000

Answer 50

For most purposes 10 is enough

Answer 51

so it is 9/1024?