Question

question 6 of 10
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. 0.20
b. 0.25
c. 0.10
d. 0.15

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability is \(P(A|B)=\frac{P(A\cap B)}{P(B)}\), where \(P(A|B)\) is the probability of event \(A\) given event \(B\), \(P(A\cap B)\) is the probability of both \(A\) and \(B\) occurring, and \(P(B)\) is the probability of event \(B\) occurring.

Let \(A\) be the event that the team goes to the state playoffs and \(B\) be the event that the team goes to the city playoffs. We are given that \(P(B) = 0.20\) and \(P(A|B)=0.50\).

Step2: Rearrange the formula to solve for \(P(A\cap B)\)

From \(P(A|B)=\frac{P(A\cap B)}{P(B)}\), we can solve for \(P(A\cap B)\) by multiplying both sides of the equation by \(P(B)\). So \(P(A\cap B)=P(A|B)\times P(B)\)

Step3: Substitute the given values into the formula

Substitute \(P(A|B) = 0.50\) and \(P(B)=0.20\) into the formula \(P(A\cap B)=P(A|B)\times P(B)\). Then \(P(A\cap B)=0.50\times0.20\)

Step4: Calculate the value

\(0.50\times0.20 = 0.10\)

Answer:

C. \(0.10\)