Answer:
[tex]\boxed{\boxed{P(\text{City playoff}\ \cap\ \text{State playoff})=0.10}}[/tex]
Step-by-step explanation:
The probability that a baseball team goes to city playoffs is 0.20.
i.e [tex]P(\text{City playoff})=0.20[/tex]
The probability that the team goes to state playoffs given that the team goes to the city playoffs is 0.50.
i.e [tex]P(\text{State playoff}\ |\ \text{City playoff})=0.50[/tex]
We know that,
[tex]P(A\ |\ B)=\dfrac{P(A\ \cap\ B)}{P(B)}[/tex]
Applying the same,
[tex]\Rightarrow P(\text{State playoff}\ |\ \text{City playoff})=0.50[/tex]
[tex]\Rightarrow \dfrac{P(\text{State playoff}\ \cap\ \text{City playoff})}{P(\text{City playoff})}=0.50[/tex]
[tex]\Rightarrow \dfrac{P(\text{State playoff}\ \cap\ \text{City playoff})}{0.20}=0.50[/tex]
[tex]\Rightarrow P(\text{State playoff}\ \cap\ \text{City playoff})={0.20}\times 0.50=0.10[/tex]
[tex]\Rightarrow P(\text{State playoff}\ \cap\ \text{City playoff})=P(\text{City playoff}\ \cap\ \text{State playoff})=0.10[/tex]
This the probability that a randomly selected team from little-town goes to the city and state playoffs.
