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# Stats problem

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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?

May 28, 2020

#1
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there are a total of 5+4=9 fish

P(catfish)=59

there are now a total of 8 fish, 4 are catfish

P(second catfish)=48=12

there are now 7 fish, 3 are catfish

P(third catfish)=37

P(fourth catfish)=26=13

P(fifth catfish)=15

to calculate the probability of catching 5 catfish
multiply the separate probabilities together

⇒P(5 catfish)=59×12×37×13×15=151890

May 28, 2020
#2
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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:

https://socratic.org/questions/a-small-pond-contains-five-catfish-and-four-bluegill-if-five-fish-are-caught-at-

May 28, 2020
#3
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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  11C =  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 / 11C =  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 11C =  35/330

To find the final answer, you must add these two intermediate results together ...

May 28, 2020