3. You have two machines in the Owl Calculator Company\'s factory that produce a

Question

3. You have two machines in the Owl Calculator Company's factory that produce all of its output. Machine A produces 47.5% of the total factory output. You determine that 96% of Machine A's output is non-defective while 2% of Machine B's output is defective. For an actuarial student, the thought of a defective calculator is horrifying! All of the calculators are compiled into one bin and then packaged. A calculator is chosen at random for testing. Given that this calculator is not defective, what is the probability that it was manufactured by Machine A? If there are 10.000 calculators in the bin, how many are defective? (a) (b)

Explanation / Answer

Answer:

a)

ND: Non defective

P( A)=0.475     P( B) = 0.525

P( ND/A) =0.96      P( ND/B) =0.98

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

=0.475*0.96+0.525*0.98

=0.9705

P( A/ND) = P( A)*P( ND/A)/P(ND)

=0.475*0.96/0.9705

=0.469861

b)

P (D) = 1-P( ND) = 1-0.9705 = 0.0295

10000*0.0295 = 295

Number of defectives = 295

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