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Answer:
P(X=3) = 0.2013
Step-by-step explanation:
After taking and tagging the first 20 birds, then we have a proportion of 20% of tagged birds within the population, that is
Supposing that the probability (0.20) of capturing a bird <em>remains constant</em>, we may resolve it as it follows:
Capturing 10 birds can be considered as a binomial experiment with a success probability p = 0.2
Let, be the expression of the binomial distribution, for our case we have:
p=0.2
x = 3
n=10
Then,
Therefore, the probability that exactly 3 of the 10 birds in the new sample were previously tagged is 20.13%