1-9.2 An electronic manufacturer uses four different types of IC\'s inmanufactur

Question

1-9.2
An electronic manufacturer uses four different types of IC's inmanufacturing a particular device. The NAND gates (designated as Gif good and G' if bad) have a probability of 0.05 of being bad. Theflip flops (F and F') have a probability of 0.1 of being bad,the counters (C and C') have a probability of 0.03 of being bad,and the shift registers (S and S') have a probability of 0.12 ofbeing bad.

D. If a particular device does not work, determine the probabilitythat both the flip flops and the counters are bad.

Answer: 0.0111

Explanation / Answer

let us denote W and W' as the device works and device doesntwork now you have to find the P(F'C'/W') i.e. given the devicedoesnot work what is the prob. that both flipflop and counters arebad now we first find P(W') P(W')=1-P(W) P(W) is the probability tht device works which will happen iall the components work [note we find P(W) since P(W') is rather complicated tocalculate since the device will not work even if one or more than 1IC fails] P(W)=P(G)*P(F)*P(C)*P(S)=0.95*0.9*0.97*0.88=0.729828 P(W')=1-P(W)=0.270172 nowP(C'F'/ W')=P(C'F' W') / P(W')=P(C'F') / P(W') P(C'F')=0.1*0.03=0.003 P(C'F'/ W')=0.003/0.270172=0.011104 hope this helps

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