Respuesta :
Answer:
The probability that the home team will win this game given that it is ahead at the half is 0.75.
Step-by-step 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. [tex]P(A)=0.60[/tex]
The home team will be ahead at half-time as well as at the final gun is 0.45.
i.e. [tex]P(A\cap B)=0.45[/tex]
The probability that the home team will win this game given that it is ahead at the half is given by,
[tex]P(B|A)=\frac{P(A\cap B)}{P(A)}[/tex]
[tex]P(B|A)=\frac{0.45}{0.60}[/tex]
[tex]P(B|A)=0.75[/tex]
Therefore, The probability that the home team will win this game given that it is ahead at the half is 0.75.
