Probability of fishes

Question

Consider a lake full of three species of fish: walleye, bass and
perch. The lake contains 800 walleye, 800 bass and 400 perch. (This population is large enough that
you can consider all samples to be sampling with replacement for any calculations).

 

 

What is the probability that if you catch 8 random fish you will get 5 walleye and 3 non-walleye fish?

The answer is : p(5W, 3non) = 0.1239

Can someone explain how to solve this problem

 

Answer 1

Hello Steins,

This is a binomial distribution. You basically look at it as a success or the probability of catching a walleye is 800 out of 2000 or .4. The probability of not catching a walleye is .6.

8C5 times (.4)^5 times (.6)^3=0.1234

ncr times (p)^r times (1-p)^(n-r)