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.
Step-by-step explanation:
Apply the following probability formula:
![P(A|B)=(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}*0.10 \\ P(state\text{ play off }\cap\text{ city play off\rparen=0.02} \end{gathered}]()
Final answer:
Thus option (B) is the correct answer.