A large pond contains fish, of which have been tagged. Biologist A takes a simple random sample of fish from the pond. Biologist B takes a simple random sample of fish from the fish that remain in the pond after Biologist A has drawn her sample. You can assume that +< . a) Fill in the blank with a math expression involving any or all of , , , and . Explain your answer. The number of tagged fish in Biologist A's sample has expectation ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ . b) Fill in the blank (carefully!) with a math expression involving any or all of , , , and . Explain your answer. The number of tagged fish in Biologist B's sample has expectation ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ . c) Fill in the blank with a math expression involving any or all of , , , and . Explain your answer. The number of tagged fish that don't get into the samples has expectation ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ .
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ask Charles Frederick Hughes