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.
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.
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:
I hope this clears your doubt.
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