Here is the problem:
A student prepares for an exam by studying a list of ten problems.
She can solve six of them. For the exam, the instructor selects five problems at random from the ten on the list given to the students. What is the probability that the student can solve all five problems on the exam?
Here is how I solved it:
I found all possible exams which is (10 choose 5) = 252
then to find the probability I calculated all possible subsets with 5 questions she can solve and got (6 choose 5) = 6
So P(a)= 6/252 = 0.0238 ? roughly 2.38%?
What am I doing wrong here, some one said that I have to use binomial probability theorem here but it can't be because that is a few chapters away in the book, there has to be a way of solving it without it... Please help
After I solved it, I found solution to this problem on the net which rated as a right one by many people, and it has a totally different answer. Here it is
And this through me off...It's a binomial probability
Here's how it would look written out:
(Total # of questions choose # of questions on actual exam)
* (Probability the student knows the answer)^(number of questions she gets right)
* (Probability she doesn't know the answer)^(number she gets wrong)
And here's how it looks with the numbers plugged in:
(10 choose 5) * (6/10)^5 * (4/10)^5
= 252 * 0.078 * 0.01
= 0.2
So there's a 20% chance she'll get them all correct.
If you have faithfully reported the correct wording of the question then, because of the simplicity of the way that question is worded, I think that it is safe to assume that there six and only six questions of the ten that she can answer.
(Suppose in a group of ten people six are female. We randomly select a committee of five from those ten. What is the probability that the committee is all female? Is that not the same question?)
In order for the solution you found to be correct the following would have to be the case. From a list of ten questions a student can work any one of them with the probability of 0.6 of being correct. Then on a test of five questions taken from that list, what is the probability she will score 100%?
Clearly, that is not what the question means. You have worked it correctly.
Pleases tell us where you found that bogus solution.