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?

Guest May 28, 2020

#1**+1 **

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

julissalazoaguilar20 May 28, 2020

#2**+3 **

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:

CalTheGreat May 28, 2020

#3**0 **

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 _{11}C_{7 } = 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):

_{4}C_{3}·_{7}C_{4} = 4·35 = 140 ways

so the probability that this happens is _{4}C_{3}·_{7}C_{4} / _{11}C_{7 } = 140/330

2) Catching exactly 4 catfish (which means that you are catching 4 of the 4 catfish and 3 of the 7 bluegill):

_{4}C_{4}·_{7}C_{3} = 1·35 = 35 ways

so the probability that this happens is _{4}C_{4}·_{7}C_{3 }/ _{11}C_{7 } = 35/330

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

geno3141 May 28, 2020