Answer:
C. 0.10
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It 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.
In this question:
Event A: Goes to the city playoffs
Event B: Goes to the state playoffs.
In Littletown, the probability that a baseball team goes to the city playoffs is 0.20.
This means that [tex]P(A) = 0.2[/tex]
The probability that the team goes to the state playoffs given that the team goes to the city playoffs is 0.50.
This means that [tex]P(B|A) = 0.5[/tex]
What is the probability that a randomly selected team from Littletown goes to the city and state playoffs?
This is [tex]P(A \cap B)[/tex]. So
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]P(A \cap B) = P(A)*P(B|A) = 0.2*0.5 = 0.1[/tex]
The correct answer is given by option C.
