# Multiple choise test probability!? Help!!

• May 3rd 2009, 02:12 PM
stephy7878
Multiple choise test probability!? Help!!
teacher give a 20 question multiple choice test. There are 4 possible answers and only one is correct. Find the probability that the student..

a) Gets exactly 19 right
b)Gets at least 1 right

I'm guessing this has to do with binomial probability.. since there is 4^20 answers.

not sure how you would set this up. Any help is appreciated!

Okay, so for A) it would be 20C19 x (.25)^19x(.75)^1 ????? I got 5.46%?????

And for B)

1- minus part A , which is 99%

Right????
• May 3rd 2009, 02:23 PM
Rapha
Hello.

Quote:

Originally Posted by stephy7878
teacher give a 20 question multiple choice test. There are 4 possible answers and only one is correct. Find the probability that the student..

a) Gets exactly 19 right
b)Gets at least 1 right

I'm guessing this has to do with binomial probability.. since there is 4^20 answers.

not sure how you would set this up. Any help is appreciated!

Okay, so for A) it would be 20C19 x (.25)^19x(.75)^1 ?????

Yup
Quote:

Originally Posted by stephy7878
I got 5.46%?????

No; 20C19 = 20, 0.25^(19) is nearly 0

Quote:

Originally Posted by stephy7878
And for B)

1- minus part A , which is 99%

Right????

Minus Part A? what? I thought your solution for A was 5.46%?

Anyway; you need to find

1 - prob("all 20 answers are incorrect") = 1 - prob("0 answers are correct")

where prob("20 anwers are incorrect") = 20C0 *0.25^0*0.75^20 = 0.003 = 0.3%