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? Type your answer below using complete sentences.

Question

campbell_st · Answer

this is a binomial probability question 

let p be a correct answer with a probability of 1/4

and q be an incorrect answer with a probability of 3/4

the probability of 3 correct from 5 can be found using 

$$^nC_{k} \times p^k \times q^{n - k}$$

I have already defined p and q

you need to know 

n = 5, k = 3

and C means combination...

hope it helps

anonymous · Answer

I still am lost can you explain it a little more clearly

campbell_st · Answer

ok... so here it is with the appropriate substitutions

and binomial probabilities uses the probability of success (p)  1/4 (providing th  correct answer from 4 choices)

 and probability of failure (q) 3/4  ( 3 incorrect answers out of 4)

so the answer is 



$$^5C_{3} \times (\frac{1}{4})^3 \times (\frac{3}{4})^{5 - 3}$$

just calculate it out...

anonymous · Answer

so what would C be

campbell_st · Answer

C stands for combination.... 

$$^5C_{3} = \frac{5!}{3! \times (5 - 3)!}$$

anonymous · Answer

Its still doesnt make any sense

campbell_st · Answer

ok... here have you studied binomial probabilities.... combinations and permuatations...?

anonymous · Answer

yes accept the last one

campbell_st · Answer

ok.... well this question is asking you to use binomial probability to calculate the solution

you may have seen the formula as 

$$\left(\begin{matrix}n \ k\end{matrix}\right) \times (p)^k \times (q)^{n - k}$$

in binomial probability there are only 2 things that can happen 

getting a right answer....P(right) = 1/4

and getting a wrong answer ....P(wrong) =3/4

you need to use both of these pieces of information to find the probability of 3 correct from 5...

is that any clearer...

anonymous · Answer

nope

campbell_st · Answer

ok... here are some notes and examples I just googled which goes through Binomial probabilities. 

hope it helps... 

then comeback and look at the question and solution

campbell_st · Answer

oops forgot the link http://www.regentsprep.org/Regents/math/algtrig/ATS7/BLesson.htm

anonymous · Answer

wow doesnt help a bit

campbell_st · Answer

ok.... well I think you need to sit down with your instructor and go though it... 



I'm confident my solution is correct...

anonymous · Answer

ok so what would you think the answer would be?