Stevie W.

asked • 08/29/21

probability stats

Suppose that a pest control program is dealing with two types of rats, black and brown.

It is found that the probability of a rat being brown, given that it is caught in a trap, is 0.85.

It is estimated that the probability of any rat being caught is 0.25 and that

the probability of a randomly chosen rat in the region being brown is 0.8.

What is the probability of a rat being caught in a trap given that it is brown?

Give your answer as a decimal accurate to 2 decimal places.


David C.

tutor
So the premise of this question is to find out that if a rat is brown, how likely it will be caught in a trap. Let's set T = trapped, or caught in a trap B = brown rat So we want to know P(T|B), or the probability of a rat being trapped, given that it is brown. We know P(B|T) = 0.85 P(T) = 0.25 P(B) = 0.8 From what we know of conditional probability, P(T|B) = P(T and B) / P(B) P(T and B) = P(B|T) * P(T) At this point, you should be able to substitute the second equation into the top part of the first. Since you have all the values: P(B|T), P(T), and P(B), you should be able to solve for the answer.
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08/29/21

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