Question

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?

Answer 1

I would use the binomial distribution method

Answer 2

ok, so, i know how to do that but, which numbers do i pull from the text?

Answer 3

We would use (n x) p^x q^(n-x)

Answer 4

where p=.25 q=.75 n=5 x=3

Answer 5

woah... I don't think i've ever used that before but I'll try it! ^^

Answer 6

by (n x) i mean n choose x

Answer 7

I got I got about 8.79%

Answer 8

Do you have the solution?

Answer 9

im not really sure how to get that, so (5x3) (2.5)^3 75 ^(5-3) ?

Answer 10

5C3 not 5x3

Answer 11

ooh, ok i got it now ^^ 5C3 is 10 right? thats what i get when i plug it in

Answer 12

yes

Answer 13

oh and p=.25 and q=.75 not 2.5 and 75

Answer 14

I can explain the binomial distribution to you if you would like

Answer 15

i get the foiling and unfoiling method, is it the same thing? I don't think i'v ever done it with exponents before

Answer 16

I am not sure what the foiling unfoiling method is.

Answer 17

For this problem I believe most people would do what I did. Although there are other ways to think about it.

Answer 18

would you mind explaining the binomial distribution, if its not to much trouble?

Answer 19

Not at all. I had a horrible professor for this stuff and taught myself... it took me forever!!

Answer 20

Ok so I like to think of the binomial distribution as basically a little shortcut we can use to find the probability of something occurring. It has many restrictions though and can only be used under certain circumstances.

Answer 21

First of all:
Each trial (or question) must have an outcome of either yes or no... in this case it was right or wrong...

Answer 22

It must consist of repeated trials that do not depend on each other... (i.e. getting the first question correct has no influence on the next question.)

Answer 23

And the probability of "yes" (or getting the question correct) must remain the same.

Answer 24

If the scenario satisfies these three things then we are allowed to use the binomial distribution.

Answer 25

You following thus far?

Answer 26

yes, so far, yes.

Answer 27

sweet!

Answer 28

Here is the formula we use to calculate probability using the binomial distribution:
\[_n C_{x}* p^x *q^{n-x}\]

Answer 29

n is the number of trials (questions)
x is the number of success we want (# of correct answers)
p is the probability of getting a success on any one of the trials
q is the probability of getting a failure on any one of the trials

Answer 30

when you plug all those numbers in the formula I posted will give you the probability of getting x successes

Answer 31

Does it make more sense now?

Answer 32

ok yes theoretically it makes sense in my head but when i go to plug it in, 5C3 * p^ (what is the exponent here?) * .75^(5-3)

Answer 33

x

Answer 34

which in this case is 3

Answer 35

we want 3 correct answers

Answer 36

p is .25.. you have a 1 in 4 chance of getting the answer correct on each trial

Answer 37

Get it?

Answer 38

sorry my computer died, yes!! I understand! thank you sososo much really!