Respuesta :
Using conditional probability, it is found that:
[tex]P(A|B^\prime) = \frac{1}{3}[/tex]
What is Conditional Probability?
Conditional probability is the probability of one event happening, considering a previous event. The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which:
- P(B|A) is the probability of event B happening, given that A happened.
- [tex]P(A \cap B)[/tex] is the probability of both A and B happening.
- P(A) is the probability of A happening.
For this problem, we are given that:
- [tex]P(B^\prime) = 1 - P(B) = 1 - \frac{1}{3} = \frac{2}{3}[/tex].
- [tex]P(A \cap B^\prime) = \frac{2}{9}[/tex]
Then:
[tex]P(A|B^\prime) = \frac{P(A \cap B^\prime)}{P(B^\prime)}[/tex]
[tex]P(A|B^\prime) = \frac{\frac{2}{9}}{\frac{2}{3}}[/tex]
[tex]P(A|B^\prime) = \frac{1}{3}[/tex]
More can be learned about conditional probabilities at https://brainly.com/question/14398287
#SPJ1
