Question

The Business People Computer Company loses a shipment of its goods because of a mistake by one of its partners. The firm has three partners (John, Anne and Sally) who could have made the mistake but cannot tell with certainty which one was responsible. On the basis of past performance, it is known that the probability that John would make such a mistake is 0.001 (if he is responsible for the shipment); the probability for Anne is 0.002; the probability for Sally is 0.001. If John is responsible for 50% of the shipments, and Anne and Sally share the rest of the shipment responsibilities equally, what is the probability that each partner was responsible for the lost shipment?

Answer 1

Probability that each partner was responsible for the lost shipment :

= ( probability that John would make such a mistake * % that John is responsible for the shipments ) +

( probability that Anne would make such a mistake * % that Anne is responsible for the shipments )+

( probability that Sally would make such a mistake * % that John is responsible for the shipments )

= ( 0.001*0.5 ) + ( 0.002*0.25 ) + ( 0.001*0.25 )

= 0.0005 + 0.0005 + 0.00025

= 0.00125

So the probability that each partner was responsible for the lost shipment is 0.00125