Probability applications of counting principles (permutations, combinations, etc.)
Hi everyone, I'd like some help please :)
1) A basket contains 7 red apples and 4 yellow apples. A sample of 3 apples is drawn. Find the probabilities that the sample contains more red than yellow apples.
So, I figure I have to find the sum of the probabilities that the sample has:
-4 red apples and 3 yellow apples, 5 red apples and 2 yellow apples, 6 red apples and 1 yellow apple, and 7 and 0 right....right?
I want to use combinations, right? Because I know that when it asked for all red apples I did (4 3) divided by (11 3)
*pretend that those numbers are on top of each other like in combination form*
and my second question...
2) given a certain number of balls, of which some are blue, pick 5 at random. thie probability that all 5 are blue is 1/2. determine the original number of balls and decide how many were blue
This one, I have no clue.