Question

Let p(a) = 0.42, p(b) = 0.17, and p(a | b) = 0.37. What is the probability of p(b | a)?

1) 0.17
2) 0.37
3) 0.42
4) Cannot be determined

Answer 1

The correct value of P(B | A) can be found using Bayes' Theorem, and it is approximately 0.14976. The options provided do not match this value, so the answer is 'Cannot be determined' based on the given choices.

Step-by-step explanation:

The question involves calculating the conditional probability of event B given event A, denoted as P(B | A). Given that P(A) = 0.42, P(B) = 0.17, and P(A | B) = 0.37, we can use Bayes' Theorem to find P(B | A). Bayes' Theorem states that P(B | A) = [P(A | B) * P(B)] / P(A). Substituting in the given values:

P(B | A) = (0.37 * 0.17) / 0.42

P(B | A) = 0.0629 / 0.42

P(B | A) = 0.14976 (approximately)

Therefore, the probability of event B given event A (P(B | A)) is neither of the provided answer options. The correct value is approximately 0.14976, which would imply that the answer to the question is 'Cannot be determined' based on the options given.