In history class, Colin and Diana both write a multiple choice quiz. there are ten questions. Each question has five possible answers.
What is the probability that
a) Colin will pass the test if he guesses an answer to each question?
b) Diana will pass the test if she studies so that she has a 75% chance of answering each question correctly?
a) This is what i did:
I used binomial distribution (i think some part of this is wrong though)
n=10 p=.5 q=.5 3 out of 5 questions right is passing = .6
the answer in the back of the book is 0.033
b) p=.75 q=.25 n=10
the answer in the back of the book is 0.980
I know the way i did this makes no sense at all because the probability of diana passing should be greater then that of Colin but this is the only way i can think of doing this.
I feel i'm messing up with the exponents.. but to pass on a 10 question test wouldn't you at least have to get 5 questions right ..?