A mutiple choice test consists 8 questions with each question having 2 possible answers. how many different ways are there to mark the answers?

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- anonymous

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no more answers

- anonymous

just one more!

- anonymous

Use the product rule.

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## More answers

- anonymous

and it would come up to?

- anonymous

you tell me?

- anonymous

she just wants answers

- anonymous

You have 8 question, and you can answer each question 2 ways, how many total ways can you answer?

- anonymous

16

- anonymous

Nope

- anonymous

its 8 questions and u can answer it 2 different ways which it doubles

- anonymous

If it were just 2 questions with 2 ways to answer, how may ways would there be to fill the test?

- anonymous

2

- anonymous

2^2

- anonymous

Actually that's a bad example. If there were 3 questions with 2 ways to answer each how many ways

- anonymous

I'm not asking you cantor ;p

- anonymous

ok :)

- anonymous

in the same way but just with 3

- anonymous

Lets say it's a true false test with 3 questions.
I can answer
True, True, True
False, True, True
True, False, True
False, False, True
True, True, False
False, True, False
True, False, False
False, False, False
Right?

- anonymous

Yeah I know that

- anonymous

So how many is that?

- anonymous

25

- anonymous

Really? Cuase I only count 8 different ways I can do the test.

- anonymous

Err Cause rather.

- anonymous

theres 8 ways but all toghether theres 25 if u count the true false's

- anonymous

No. There are 8 different possible ways to complete the test.

- anonymous

25 ????????????????

- anonymous

So for your original question if you have 8 questions, how many possible ways can you complete the test?

- anonymous

should i ask ?

- anonymous

if u count them all toghether u get 25 thats how so stop u guys are suppose to help not be mean

- anonymous

sorry i was talking to polpak

- anonymous

w.e bye someone else will help me

- anonymous

Giving you the answer doesn't help you

- anonymous

well when it's done and outta the way I will not have to look back at it so..

- anonymous

except when it's time to take the test, or when something new is taught that uses this to solve, etc.

- anonymous

Everything builds on everything else

- anonymous

ur helping everyone else and giving them answeers?

- anonymous

pol, she added up all of them, she cant count either , there are 24 in that list

- anonymous

Yeah

- anonymous

there's 25

- anonymous

no theres 24

- anonymous

There are 8 lines, with 3 words on each line.

- anonymous

This is one of those things you got someone to tell you and didn't look back about I can see.

- anonymous

i didnt even think of that,

- anonymous

\[8\times 3 \ne 25\]

- anonymous

right

- anonymous

pol, so your integration seems redundant

- anonymous

hrm?

- anonymous

its 2 not 3

- anonymous

You talking about your u-sub question? please ask over there.

- anonymous

well, 8*2 is certainly not 25.

- anonymous

sure

- anonymous

you mean 8 *3

- anonymous

its 16

- anonymous

she cant count and doesnt reason well.

- anonymous

I do mean 8*3, but she claimed it was 2, not 3.

- anonymous

the problem states 3 not 2

- anonymous

wait, i guess theres some subtley here. let me see

- anonymous

2 not 3

- anonymous

Erg. Ok look chika.
I enumerated the possible outcomes for a test with 3 questions where each question had 2 answers.

- anonymous

ok each of those lines is ONE possibility for the test to be solved

- anonymous

Each line in my post was a way you could complete the whole test. Not one question.

- anonymous

so you wrote out the entire sample space

- anonymous

Try something more simple. If you have two true or false questions how many ways can you answer them?

- anonymous

I didn't want to try to write out the sample space for 8 questions because a) that would have given her the answer, and b) I didn't want to write 256 lines.

- anonymous

the other way is to use multiplication rule
for the first question there are 2 ways, second question there are 2 ways to answer, etc,
so the total ways is 2 x 2 x 2 ...

- anonymous

kind of like a tree diagram

- anonymous

so you can enumerate the entire space, as you did pol for your simpler example. or you can use product rule rather than enumerate 256 cases

- anonymous

o wait

- anonymous

I got it

- anonymous

http://www.khanacademy.org/v/probability--part-2?p=Probability

- anonymous

chika, how did you get 25 !!!

- anonymous

i got the answer

- anonymous

pol, it is redundant because you already have cos z dz in the numerator

- anonymous

du = cos z dz, and you already have cos z dz in the numerator

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