The probability of generating more than $300k in Non-Full Season ticket revenue

Question

The probability of generating more than $300k in Non-Full Season ticket revenue for a regular season game, given that the game is on a Friday, is 73%. The probability of generating less than $300k in Non-Full Season ticket revenue for a regular season game, given that the game is NOT on a Friday is 53%. The probability that a regular season game is on a Friday is 14%. What is the probability that a regular season game is not on a Friday, given that the game generates more than $300k in Non-Full Season ticket revenue?                                      

Explanation / Answer

probabilty of generating nore then 300 =P(A|B)=0.73

Probabilty that game is on friday =P(B)=0.14

probability of generating less than $300k in Non-Full Season ticket revenue for a regular season game, given that the game is NOT on a Friday =P(Ac|Bc)=0.53

hence P(A|Bc)=1-0.53=0.47

there fore P(A)=P(B)*P(A|B)+P(Bc)*P(A|Bc)=0.14*0.73+0.86*0.53=0.558

hence probability that a regular season game is not on a Friday, given that the game generates more than $300k in Non-Full Season ticket revenue =P(Bc|A)=P(Bc)*P(A|Bc)/P(A)=0.86*0.53/0.558=0.8187

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