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A fish tank in a pet store has 15 fish in it. 11 are orange and 4 are white. How do I determine the probability that if we select 3 fish from the tank, at least 2 will be white?

Question

A fish tank in a pet store has 15 fish in it. 11 are orange and 4 are white. How do I determine the probability that if we select 3 fish from the tank, at least 2 will be white?

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Step 1

The Hypergeometric distribution:

A random variable X is said to follow hypergeometric distribution if its probability mass function is as follows,

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Step 2

Computing the probability of getting 3 fish from the tank, at least 2 will be white:

Here 3 fishes are selected from a tank containing 15 fishes.

This follows Hypergeometric distribution with N=15, K = 4, k = 2,..., n and n = 3.

Here, the total number of fishes is denoted by N, the total number of white fishes is denoted by K and number of observed successes by k.

Then the ...

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