2. Solve by simulating the problem.

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

2. Solve by simulating the problem.
 
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.

reemii · Answer

5 questions, 4 choices for each.
The probability of having a good answer at one particular question is 1/4, because the choice is random, and there are 4 choices.

The experience "choose an answer" is repeated 5 times.

This is a binomial experiment ($\text{Bin}(n,p)$). Does this help ?

anonymous · Answer

no

anonymous · Answer

haha sorry im just horrible at probablities

reemii · Answer

what do they mean by "solve by simulating?"

Are you allowed to use a formula ? now i think you're not.

In that case, we need to do this (C: correct, W: wrong):
the possible outcomes with 3 good answers exactly
CCCWW
CCWCW
CCWWC
...
..

write them all.
Then you compute the probability of having 3 good answers as the sume of hte probabilities of each separate case that you wrote just above.

P(3 correct out of 5)
= P(CCCWW) + P(CCWWC) + ...
= (1/4)(1/4)(1/4)(3/4)(3/4) + (1/4)(1/4)(3/4)(1/4)(3/4) + ...
= $\pi + \pi + ...$

Since all these values are equal, you only need to know how many there are ($n$). The answer will be $n\times \pi$.