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

Option: D is the correct answer.
D) 0.10
Let A denote the event that the baseball team goes for city playoffs.
B denote the event that the baseball team goes for state playoffs.
A∩B denote the event that the team goes for city and state playoffs.
Let P denote the probability of an event.
We are given P(A)=0.20
P(B|A)=0.50
We know that:
[tex]P(B|A)=\dfrac{P(A\bigcap B)}{P(A)}\\\\\\P(A\bigcap B)=P(B|A)\times P(A)\\\\\\P(A\bigcap B)=0.20\times 0.50\\\\\\P(A\bigcap B)=0.10[/tex]
Hence, the probability that a randomly selected team from Little town goes to the city and state playoffs is:
D) 0.10
Answer: Option 'D' is correct.
Step-by-step explanation:
Since we have given that
Probability that the base ball team goes to the city playoffs P(C) = 0.20
Probability that the team goes to the state playoffs given that the team goes to the city playoffs P(S|C) = 0.50
We need to find the probability that the baseball team goes to both state and city i.e. P(C∩S)
Since we have given the conditional probability.
So, we will apply the formula of it.
[tex]P(S\mid C)=\dfrac{P(S\cap C)}{P(C)}\\\\0.50=\dfrac{P(C\cap S)}{0.20}\\\\0.50\times 0.20=P(C\cap S)\\\\0.10=P(C\cap S)[/tex]
Hence, Option 'D' is correct.