probability

Question

The data Baseball contains information about a team which is using an automatic pitching machine.
If the machine is correctly setup and properly adjusted, it will strike 85 percent of the time. If it is
incorrectly set up, it will strike only 35 percent of the time. Past data indicates that 75 percent of the
setup of the machine is correctly done. After the machine has been set up, at batting practice one
day, it throws three strikes on the first three pitches. What is the revised probability that has setups
done correctly?

Event P(Event) = 0.75 (correct) ; 0 (incorrect)

P(1 Strike/Event) = 0.85 (correct) ; 0.35(incorrect)

Answer 1

Have to use Bayes' theorem to solve this problem.

 

C= event that the setup was done correctly

I =  .... incorrectly

S = event that it will strike

3S = event that it will strike on first 3 pitches

P( C| 3S) = P(3S|C)*P(C) / [ P(3S|C)*P(C) +  P(3S|I)*P(I) ]

 

             = [(0.85)^3 * 0.75 ] / [ (0.85)^3 * 0.75  + (0.35)^3 * 0.25 ]