Question

Knowing that the probability of an event A is 0.25, the probability of an event B is 0.2, and the probability of B given A is 0.37, what is the probability of A given B? Provide your answer with 3 decimal places.

a. 0.342
b. 0.279
c. 0.098
d. 0.165

Answer 1

After applying Bayes' theorem with the given probabilities, the probability of A given B is calculated as 0.4625, which doesn't match any of the provided options.

Step-by-step explanation:

To find the probability of A given B, denoted as P(A|B), we use Bayes' theorem. The formula we use is P(A|B) = P(B|A) × P(A) / P(B). We are given: P(A) = 0.25, P(B) = 0.2, and P(B|A) = 0.37.

Using these values, we calculate P(A|B) as follows:

1. P(A|B) = P(B|A) × P(A) / P(B)
2. P(A|B) = 0.37 × 0.25 / 0.2
3. P(A|B) = 0.0925 / 0.2
4. P(A|B) = 0.4625

So, the probability of A given B is 0.4625. However, this answer is not among the options provided, suggesting there may have been a misunderstanding in the initial conditions or a miscalculation.