Which of the following random variable can be modelled with a binomial distribution? 1) The number of tagged fish if a fisherman randomly catches 20 fish without replacement from a pond of many fish. It is known that 20% of the fish have been tagged. 2) The number of tagged fish if a fisherman randomly catches 20 fish without replacement from a pond of 50 fish. It is known that 20% of the fish have been tagged. 3)The number of tagged fish out of 20 that a fisherman randomly catches with replacement from a pond of 50 fish. It is known that 20% of the fish have been tagged. 4) The number of fish a fisherman has to catch randomly with replacement so that 20 fish that have been tagged are caught from a pond of many fish. It is known that 20% of the fish have been tagged.

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Which of the following random variable can be modelled with a binomial distribution?

1) The number of tagged fish if a fisherman randomly catches 20 fish without replacement from a pond of many fish. It is known that 20% of the fish have been tagged.

2) The number of tagged fish if a fisherman randomly catches 20 fish without replacement from a pond of 50 fish. It is known that 20% of the fish have been tagged.

3)The number of tagged fish out of 20 that a fisherman randomly catches with replacement from a pond of 50 fish. It is known that 20% of the fish have been tagged.

4) The number of fish a fisherman has to catch randomly with replacement so that 20 fish that have been tagged are caught from a pond of many fish. It is known that 20% of the fish have been tagged. 

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