Question

According to the general equation for conditional probability, if P(AB) = and P(B) = 2, what is P(A/B)? 12 O A. 3/ О в. 4 O c. 2/ C. 5 O D. 9

Answer 1

Using conditional probability, it is found that:

$P(A|B^\prime) = \frac{1}{3}$

What is Conditional Probability?

Conditional probability is the probability of one event happening, considering a previous event. The formula is:

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which:

• P(B|A) is the probability of event B happening, given that A happened.

• $P(A \cap B)$ is the probability of both A and B happening.

• P(A) is the probability of A happening.

For this problem, we are given that:

• $P(B^\prime) = 1 - P(B) = 1 - \frac{1}{3} = \frac{2}{3}$.

• $P(A \cap B^\prime) = \frac{2}{9}$

Then:

$P(A|B^\prime) = \frac{P(A \cap B^\prime)}{P(B^\prime)}$

$P(A|B^\prime) = \frac{\frac{2}{9}}{\frac{2}{3}}$

$P(A|B^\prime) = \frac{1}{3}$

More can be learned about conditional probabilities at brainly.com/question/14398287

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