# i hope i make JohnM and quark proud

#### hilarysears77

##### New Member

okay i managed to do a bonus question on my "take home test" (which is kinda .
I just want to see if I did it right and answered it right bare with me....
IF I DID NOT DO OR ANSWER IT RIGHT DO NOT TELL ME HOW!!!

A student takes a 9 question multiple choice test by guessing. Each question has 5 choices. What is the probability that at least 4 are correct?

P(X) =
n! x (n-x)
_________ *p * q
(n-x)!x!
n=9
x=4
p=4/9
q=5/9

using these values,
i got 26%
please tell me I did this correct
And I do want to know how you are making out of this website, because i told everybody in my statistics class!!!!!
p.s

#### JohnM

##### TS Contributor
We're always proud of students who try!

With this problem, you started on the right track. Make sure the binomial formula includes p^x and q^(n-x).

p = probability of success
q = 1-p

You need to think how "success" is defined in this problem - it's the probability of getting 1 question correct by guessing the correct answer out of 5 choices.

Then you need to find the probability of getting 0 correct, 1 correct, 2 correct, and 3 correct. Add these up, then subtract this sum from 1.

In a binomial probability distribution (any distribution, for that matter), the sum of all the probabilities equal 1. So, the probability of getting 4 or more correct is equal to 1 minus the probability of getting 3 or less.

#### quark

Hilary,

Since there are five choices in each question, p=1/5, and q=4/5.

#### hilarysears77

##### New Member
woo hoo (I hope)

64.42%

is this it?????????
hilary

#### JohnM

##### TS Contributor
Hilary,

The probability of:

0 correct = 0.1342
1 correct = 0.302
2 correct = 0.302
3 correct = 0.1762

Add these up and subtract the sum from 1.

The answer is 0.0856, or around 8.5% chance of guessing 4 or more questions correctly.

Think it through - if you had to completely guess on 9 questions, and the probability of getting any particular question correct is only 20%, it's going to be really hard to guess 4 or more correctly.

#### hilarysears77

##### New Member
finally figured it out, just read and think it through

okay
i did not have to change p=1/5 and q=4/5
i just had to change the
n! / (n-X)X! formula
n=9
and x=0, x=1, x=2, x=3, for each formula
and the p^n and q^(n-x)

i finally figured it out thanks sgain
p.s I am still stuck on the 175 words per minute,with a standard dev. of 20, the top 3% of the class is to receive a special award, what is the min
but do not tell me, you have helped me enough. I will get it and let you know what I come up with

thanks again quark and JohnM