A biologist captures $21$ grizzly bears during the spring, and fits each with a radio collar. At the end of summer, the biologist is to observe $15$ grizzly bears from a helicopter, and count the number that are radio collared. This count is represented by the random variable X.
Suppose there are $114$ grizzly bears in the population.
The biologist gets back from the helicopter observation expedition, and was asked the question: How many radio collared grizzly bears did you see? The biologist cannot remember exactly, so responds " somewhere between $4$ and $9$ (inclusive) ".
Given this information, what is the probability that the biologist saw $7$ radio-collared grizzly bears?
Would this just be conditional probability? I.E
$A$ = Event that biologist saw between $4$ and $9$ Radio collared bears
$B$ = Event that the biologist saw $7$ radio collared bears
And the probability is just $P( A|B )$?