Jansen Electronics has four machines that produce identical components for use i

Question

Jansen Electronics has four machines that produce identical components for use in its DVD players. The proportion of the components produced by each machine and the probability of a component produced by that machine being defective are shown in the accompanying table. (Round your answers to three decimal places.) Proportion of Probability of Machine Components Produced Defective Component 0.10 0.35 0.35 0.20 0.02 0.04 0.02 0.04 IV (a) What is the probability that a component selected at random is defective? (b) What is the probability that a component selected at random was produced by Machine I, given that it is fctive? (c) what is the probability that a component selected at random was produced by Machine , given that it is defective?

Explanation / Answer

Solution:-
= A P[m/c I & defective] = 0.10*0.02 = 0.002  
= B P[m/c II & defective] = 0.35*0.04 = 0.014
= C P[m/c III & defective] = 0.35*0.02 = 0.007
= D P[m/c IV & defective] = 0.20*0.04 = 0.008

(a) P[defective] = E = A+B+C+D = 0.002 + 0.014 + 0.007 + 0.008 = 0.031

(b) P[m/c I | defective] = A/E = 0.002/0.031 = 0.065

(c) P[m/c II | defective] = B/E = 0.014/0.031 = 0.452

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