Binomial Probability Distributions

[msmarvelous]

Hi,
I'm having some trouble understanding what method to use to find the answer.


A multiple choice test has 15 questions each with 5 alternatives. Assume that a student answers all questions by random guessing. Determine the following probabilities.

A) P(no more than 5 correct)
B) P(exactly 5)
C) P(more than 5 correct)

 

[quintopia]

Hi, perhaps the following will make these easier:

P(no more than 5)=1-P(at least 6)=1-(ways to choose 6 problems)*(probability of getting those 6 correct)
[because once you've chosen 6 to be correct, you have at least 6 correct and the rest don't matter]
P(exactly 5)=(ways to choose 5)*(probability of getting those 5 right)*(probability of getting the rest wrong)
[in this case, the rest do matter. . .they all have to be wrong]
P(more than 5)=1-P(no more than 5)