Question

Suppose that for a certain football game the probability that the home team will be ahead at half-time is 0.60 and the probability that the home team will be ahead at half-time as well as at the final gun is 0.45. What is the probability that the home team will win this game given that it is ahead at the half?

Answer 1

The probability that the home team will win this game given that it is ahead at the half is 0.75.

Explanation:

Given : Suppose that for a certain football game the probability that the home team will be ahead at half-time is 0.60 and the probability that the home team will be ahead at half-time as well as at the final gun is 0.45.

To find : What is the probability that the home team will win this game given that it is ahead at the half?

Solution :

Let A be the event ahead at the half-time.

Let B be the event ahead at the end of the game.

The home team will be ahead at half-time is 0.60.

i.e.
`P(A)=0.60`

The home team will be ahead at half-time as well as at the final gun is 0.45.

i.e.
`P(A\cap B)=0.45`

The probability that the home team will win this game given that it is ahead at the half is given by,

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

`P(B|A)=(0.45)/(0.60)`

`P(B|A)=0.75`

Therefore, The probability that the home team will win this game given that it is ahead at the half is 0.75.