What is the probability that the rabbit was picked from Cage 1?

What is the probability of picking a rabbit from Cage 1 given that a rabbit was picked?

As per the given statement, the correct option is 1/4. The probability that the rabbit was picked from Cage 1 given that a rabbit was picked is 1/4. To solve this problem, we can use Bayes' theorem to calculate the probability.

Bayes' Theorem Calculation

Events: A: Picking a rabbit from Cage 1 B: Picking a rabbit

Calculation:

We want to find P(A|B), the probability that the rabbit was picked from Cage 1 given that a rabbit was picked. Using Bayes' theorem: P(A|B) = P(B|A) * P(A) / P(B) P(B|A) = 5/20 = 1/4 (probability of picking a rabbit given selecting from Cage 1) P(A) = 1/2 (probability of selecting Cage 1) P(B) = 15/20 = 3/4 (overall probability of picking a rabbit) Substituting these values into Bayes' theorem: P(A|B) = (1/4) * (1/2) / (3/4) P(A|B) = 1/6 / (3/4) P(A|B) = 1/6 * 4/3 P(A|B) = 4/18 P(A|B) = 1/4 Therefore, the probability that the rabbit was picked from Cage 1 given that a rabbit was picked is 1/4. This calculation shows how Bayes' theorem can be used to determine probabilities in such scenarios.
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