A small pond contains four catfish and seven bluegill. If seven fish are caught at random, what is the probability that at least three catfish have been caught?
there are a total of 5+4=9 fish
there are now a total of 8 fish, 4 are catfish
there are now 7 fish, 3 are catfish
to calculate the probability of catching 5 catfish
multiply the separate probabilities together
There are a total of 11 fish, @above.
I don't think you're supposed to copy and paste answers from other sites. They have different problems sometimes.
I believe you copied from here:
There are 4 catfish and 7 bluegill for a total of 4 + 7 = 11 fish.
You are selecting 7 of these 11 fish; this can be done in 11C7 = 330 ways.
You want to catch at least 3 of the 4 catfish.
This can be done in two ways:
1) Catching exactly 3 catfish (which means that you are catching 3 of the 4 catfish and 4 of the 7 bluegill):
4C3·7C4 = 4·35 = 140 ways
so the probability that this happens is 4C3·7C4 / 11C7 = 140/330
2) Catching exactly 4 catfish (which means that you are catching 4 of the 4 catfish and 3 of the 7 bluegill):
4C4·7C3 = 1·35 = 35 ways
so the probability that this happens is 4C4·7C3 / 11C7 = 35/330
To find the final answer, you must add these two intermediate results together ...