A television network earns some money each season for a hit program and loses ea

Question

A television network earns some money each season for a hit program and loses each season for a flop. In general, 19% of the programs are considered hits and 81% of the programs are flops.

A research firm will analyze the pilot episode and issue a report predicting whether the program is going to be a hit or a flop. From the past data, if the program is going to be a hit, there is a 90% chance that the research firm predicted it is going to be a hit. On the other hand, there is 20% chance the research firm predicted that the program is going to be a hit, but ended as a flop.

Calculate the appropriate conditional probabilities that the research firm will predict a hit program and a flop program.

Explanation / Answer

Ans:

P(program hit)=0.19

P(program flops)=0.81

P(research firm perdicted hit/program hit)=0.9

So,

P(research firm perdicted flop/program hit)=1-0.9=0.1

P(research firm perdicted hit/program flop)=0.2

So,

P(research firm perdicted flop/program flop)=1-0.2=0.8

A=program hit

B=perdicted hit

P(A/B)=P(B/A)*P(A)/P(B)

Now,

P(B)=P(perdicted hit)=P(perdicted hit/hit)*P(hit)+P(perdicted hit/flop)*P(flop)

=0.9*0.19 +0.2*0.81=0.333

P(perdicted flop)=1-0.333=0.667

P(program hit/perdicted hit)=(0.9*0.19)/0.333=0.5135

P(program flop/perdicted hit)=1-0.5135=0.4865

P(program hit/perdicted flop)=P(perdicted flop/program hit)*P(program hit)/P(perdicted flop)

=(0.1*0.19)/0.667=0.0285

P(program flop/perdicted flop)=1-0.0285=0.9715

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