Question

If the New England Patriots get home-field advantage, you believe there is a 60% probability they will make it to the Super Bowl. If not, this probability is only 30%. Assuming a 70% probability that the Patriots get home-field advantage, what is the probability they will make it to the Super Bowl?

Answer 1

There is a 51% probability they will make it to the super bowl.

Explanation:

We have these following probabilities:

A 70% probability that the Patriots get homefield advantage.

A 30% probability that the Patriots does not get homefield advantage.

If they get homefield advantage, a 60% probability of making the Super Bowl.

If they do not get homefield advantage, a 30% probability of making the Super Bowl.

What is the probability they will make it to the Super Bowl?

This is 60% of 70%(when they get homefield advantage and make the super bowl), and 30% of 30%(no homefield, no super bowl). So

`P = 0.6*0.7 + 0.3*0.3`

`P = 0.51`

There is a 51% probability they will make it to the super bowl.