Question

In Littletown, the probability that a baseball team goes to the city playoffs is

0.20. The probability that the team goes to the state playoffs given that the
team goes to the city playoffs is 0.50.
What is the probability that a randomly selected team from Littletown goes to
the city and state playoffs?
A. 0.15
B. 0.25
C. 0.10
Ο Ο
D. 0.20
SUBMIT

Answer 1

C. 0.10

Explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

`P(B|A) = (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.

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
`P(A) = 0.2`

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
`P(B|A) = 0.5`

What is the probability that a randomly selected team from Littletown goes to the city and state playoffs?

This is
`P(A \cap B)`. So

`P(B|A) = (P(A \cap B))/(P(A))`

`P(A \cap B) = P(A)*P(B|A) = 0.2*0.5 = 0.1`

The correct answer is given by option C.