Question

# On a given weekend in the fall, a tire company can buy television and advertising time...

On a given weekend in the fall, a tire company can buy television and advertising time for a college football game, a baseball game, or a professional football game. If the company sponsors the college football game, there is a 80% chance of a high rating, a 60% chance if they sponsor a baseball game, and a 60% chance if they sponsor a professional football game. The probabilities of the company sponsoring these various games are 0.4,0.1, and 0.5 respectively. suppose the company does get a high rating, find the probability that it sponsored a professional football game.

Hello

Let A be the event that the company got high ratings.

Let X be the event that it has sponsored a college football game.

Let Y be the event that it has sponsored a baseball game.

Let X be the event that it has sponsored a professional football game.

Given:

P(X) = 0.4 , P(Y) = 0.1, P(Z) = 0.5 , P(A|X) = 0.8 , P(A|Y) = 0.6 , P(A|Z) = 0.6

To find : P(X|A)

We know that

So, combining these 2 formulas, we get :

Now, using total probability formula:

Hence,

and hence,

I hope this clears your doubt.

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