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.