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?
PLEASE HELP ME!

Answer 1

will anyone please help?

Answer 2

What does your teacher mean by "simulating" the problem? Do you need this solved in paper or brute forced with a computer?

Answer 3

idk i am taking exam online and this is the question they gave me..

Answer 4

What's the exam for? I'm trying to figure out how they want you to solve this one.

Answer 5

prealgebra part 2

Answer 6

What is the experimental probability that you will guess exactly three out of five questions correctly?------ thats what they are asking me to figure out :/

Answer 7

Think I'm gonna go with the old fashioned solution then. To begin with, what's the probability of guessing just one question correctly?

Answer 8

i dont know :(

Answer 9

Tell you what, this does sound much more advanced than pre algebra. Let's give it a go anyway. You have four choices, and you pick one at random. What's the chance you'll be right?

Answer 10

1/4

Answer 11

There we go. Now suppose we have two questions, four answers each, and we have no idea what the answer is. What's the chance we'll guess both correctly?

Answer 12

1/2 or 2/4

Answer 13

Nope... we have 4 possible guesses for the 1st question, and for each of these we have other 4 possible guesses for the 2nd.

Answer 14

?

Answer 15

The questions are different, they're unrelated. Say we pick the first answer for the first question; then we can still pick any of the four answers for the other, and we don't know which one it is.

Answer 16

im confused how are we supposed to use that to answer my questionlol idk im lost

Answer 17

So our choices are

Answer 18

and the same if we pick 3 or 4 for the 1st question

Answer 19

woah!

Answer 20

This way, we have 16 possible answers, and only one is right

Answer 21

so 20 answers for 5 questions?

Answer 22

For 2 questions, we have 4*4 = 16
for 3 questions, we'd have 4*4*4 = 64
and so on

Answer 23

So, still with the 2 question case for now, what's the chance we'll guess both right?

Answer 24

sorry there was an inconvence
just a sec let me think

Answer 25

idk.. im dumb just warning you

Answer 26

Nah this is just not what I'd expect in a prealgebra test. Anyway, we have 16 choices: 4 for the first question, and for each of these we have other 4 for the second one. Of those choices, only one will give us both correct answers, so only one is right. What's the chance we'll pick the correct option out of 16?

Answer 27

1/4??????????????????

Answer 28

or 1/2

Answer 29

We have 16 total choices, only one is right, so the chance to pick it will be 1/16.

Answer 30

oh. brb

Answer 31

back sorry, i dont work good when im sick im back though

Answer 32

So we have the answer for 2 questions, we're getting there. Let's add one more. We haven't the slightest idea what the answer to that question is either, so we'll have to guess it too.

Answer 33

okay

Answer 34

Now we have 3 questions. For each of the 16 cases found earlier, we now have 4 new choices. So, how many choices are we going to have?

Answer 35

uhhhhhhhhhh 64?

Answer 36

wait 1024 choices for 5 question is that it!?!?!?

Answer 37

Yep. Of these 64, only one will give us the correct answers to all questions. So, given three questions with four answers each, what's the chance we'll ace the test?

Answer 38

because 4*4*4*4*4=1024
please tell me im right

Answer 39

Yeah, we'll get there soon

Answer 40

YAY okay..

Answer 41

But they asked us to find the chance to guess exactly three out of five questions correctly, not guess all five.

Answer 42

D: i thought i finally had something dang it.. so how do we find the chance to ace the test with 64 answers to 3 questions?

Answer 43

64 total answers, only one is right. What's the chance we'll pick it?

Answer 44

holy crap..uhhh 1 in a million?

Answer 45

Hah it's hard to ace that test, but not that hard... if there are 64 possibilities, chances are we'll pick the right one 1 time out of 64

Answer 46

the kid who is taking this test will fail lol

Answer 47

So the chance is 1/64

Answer 48

No wonder, he's guessing all questions... Little bastard couldn't study even one

Answer 49

lololol ok back to work lolol

Answer 50

Fair enough. Now let's add a fourth question, but this time the kid isn't gonna get it right; he's gonna screw it up.

Answer 51

Because we need him to guess only 3 out of 5, he has to get this one wrong

Answer 52

lol

Answer 53

256 choices so 1/256

Answer 54

There are indeed 256 cases, but 1/256'd be the chance of him guessing the 4 questions correctly. We can't have that

Answer 55

oh..

Answer 56

For a single question, the chance of getting it right is 1/4. What's the chance of getting it wrong?

Answer 57

1 or 3/4 or 4/4 either those

Answer 58

but i think 3/4

Answer 59

Right. The question has 4 answers, 1 is right and 3 are wrong; the chance of picking the right one is 1/4, and the chance of picking the wrong one is 3/4.

Answer 60

We need him to pick the right one for the first three questions, and the wrong one for the fourth. The chance of that will be
\[\frac{ 1 }{ 4 }*\frac{ 1 }{ 4 }*\frac{ 1 }{ 4 }*\frac{ 3 }{ 4 }\]

Answer 61

lol he is screwed

Answer 62

He partied a bit hard, no time left for studying. Can you work out that fraction for me?

Answer 63

uhhh sorry im back

Answer 64

brb ima get my good calculator

Answer 65

back okay give me a sec

Answer 66

3/256

Answer 67

Indeed, we're finally getting there. Now we add the last question. We know he has to get this one wrong too.

Answer 68

So, the chance of him getting the first three questions right (1/4) AND the two last questions wrong (3/4) will be
1/4 * 1/4 * 1/4 * 3/4 * 3/4

Answer 69

Find out that one, we're almost done here

Answer 70

i got 0.008789063

Answer 71

Hah, we'll want to keep it in fraction form for now

Answer 72

Multiply the numerators and denominators separately if your calc won't do taht

Answer 73

6/1024

Answer 74

That's 3*3 we want, not 3+3

Answer 75

omg sorry LOL 9/1024