Question

In littletown, the probability that a baseball team goes to city playoffs is 0.20. the probability that the team goes to state playoffs given that the team goes to the city playoffs is 0.50. what is the probability that a randomly selected team from littletown goes to the city and state playoffs.

a. 0.20
b. 0.15
c. 0.10
d. 0.25

mind explaining it as well?

Answer 1

0.10 (c)

for some people it could be 0.06

just letting you know

Answer 2

`\boxed{\boxed{P(\text{City playoff}\ \cap\ \text{State playoff})=0.10}}`

Explanation:

The probability that a baseball team goes to city playoffs is 0.20.

i.e
`P(\text{City playoff})=0.20`

The probability that the team goes to state playoffs given that the team goes to the city playoffs is 0.50.

i.e
`P(\text{State playoff}\ |\ \text{City playoff})=0.50`

We know that,

`P(A\ |\ B)=(P(A\ \cap\ B))/(P(B))`

Applying the same,

`\Rightarrow P(\text{State playoff}\ |\ \text{City playoff})=0.50`

`\Rightarrow \frac{P(\text{State playoff}\ \cap\ \text{City playoff})}{P(\text{City playoff})}=0.50`

`\Rightarrow \frac{P(\text{State playoff}\ \cap\ \text{City playoff})}{0.20}=0.50`

`\Rightarrow P(\text{State playoff}\ \cap\ \text{City playoff})={0.20}* 0.50=0.10`

`\Rightarrow P(\text{State playoff}\ \cap\ \text{City playoff})=P(\text{City playoff}\ \cap\ \text{State playoff})=0.10`

This the probability that a randomly selected team from little-town goes to the city and state playoffs.