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Three machinesE1, E2 and E3 in a certain factory producing electric bulbs, produce 50%, 25% and 25% respectively, of the total daily output of electric bulbs. It is known that 4% of the bulbs produced by each of machines E1 and E2 are defective and that 5% of those produced by machine E3are defective. If one bulb is picked up at random from a day’s production, calculate the probability that it is defective.

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`B_1` is the event when`E_1` produces bulbs
`B_2` is the event when`E_2` produces bulbs
`B_3` is the event when`E_3` produces bulbs
E event when a defective bulb is selected
`P(B_1)=1/2,P(B_2)=1/4,P(B_3)=1/4`
`P(E/B_1)=1/25,P(E/B_2)=1/25,P(E/B_3)=1/20`
Probability of event E when`B_1` has already occured
`P(E)=P(B_1)(P(E/B_1)+P(B_2)*P(E/B_2)+P(B_3)*P(E/B_3)`
`=1/2*1/25+1/4*1/25+1/4*1/20`
`P(E)=17/400`.

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