Question

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

Answer 1

Answer: Option 'D' is correct.

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.

`P(S\mid C)=(P(S\cap C))/(P(C))\\\\0.50=(P(C\cap S))/(0.20)\\\\0.50* 0.20=P(C\cap S)\\\\0.10=P(C\cap S)`

Hence, Option 'D' is correct.

Answer 2

Option: D is the correct answer.

D) 0.10

Explanation:

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:

`P(B|A)=(P(A\bigcap B))/(P(A))\\\\\\P(A\bigcap B)=P(B|A)* P(A)\\\\\\P(A\bigcap B)=0.20* 0.50\\\\\\P(A\bigcap B)=0.10`

Hence, the probability that a randomly selected team from Little town goes to the city and state playoffs is:

D) 0.10