(1) A lake contains 26 lake trout. Twelve are captured, tagged, and released. A certain
time later, 5 of the 26 are captured. What is the probability that exactly one of them
is tagged? State clearly what assumptions you are using.
Answers
Given : A lake contains 26 lake trout. Twelve are captured, tagged, and released.
A certain time later, 5 of the 26 are captured.
To Find : probability that exactly one of them is tagged
Solution:
Total = 26
Tagged = 12
untagged = 26 - 12 = 14
5 of the 26 are captured.
Number of Ways = ²⁶C₅
exactly one of them is tagged
one to be selected from 12 tagged
and 4 to be selected from 14 untagged.
= ¹²C₁*¹⁴C₄
probability that exactly one of them is tagged = ¹²C₁*¹⁴C₄ / ²⁶C₅
= 0.1826
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