Question

In Littletown, the probability that a baseball team goes to the city playoffs is0.20. The probability that the team goes to the state playoffs given that theteam goes to the city playoffs is 0.10.What is the probability that a randomly selected team from Littletown goes tothe city and state playoffs?A. 0.50B. 0.02C. 0.10D. 0.06

Answer 1

Given:

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 0.10.

$\begin{gathered} P(city\text{ playoff\rparen=0.20} \\ P(state\text{ playoff \mid city play off}\operatorname{\rparen}\text{=0.20} \end{gathered}$

Required:

Find the probability that a randomly selected team from Littletown goes to the city and state playoffs.

Explanation:

Apply the following probability formula:

$P(A|B)=\frac{P(A\cap B)}{P(B)}$$\begin{gathered} P(state\text{playoff}\operatorname{\mid}\text{c}\imaginaryI\text{typlayoff}\operatorname{\rparen}=\frac{P(state\text{ play off }\cap\text{ city play off\rparen}}{P(city\text{ play off\rparen}} \\ 0.10=\frac{P(state\text{ play off }\cap\text{ city play off\rparen}}{0.20} \\ P(state\text{ play off }\cap\text{ city play off\rparen=0.20}\times0.10 \\ P(state\text{ play off }\cap\text{ city play off\rparen=0.02} \end{gathered}$

Final answer:

Thus option (B) is the correct answer.