Transistors are produced by a process in which 307. are electrically detective (

Question

Transistors are produced by a process in which 307. are electrically detective (E) and 407. have dented cans (C) prior to assembly. Assume they are rejected for either reason. What is the probability that transistor chosen at random will be a reject ? suppose the electrical defects fall into two categories corresponding to a collector current which either too low (E_1) on too high (E_2). If P(E_1) = 0.1, P(E_2) = 0.2 (and P(C) = 0.4 as before), what is the probability of finding reject if we reject for either or both E_1 and C? What is it if we reject for either E_1, E_2, C or all?

Explanation / Answer

here probability of electrically defective =P(E) =0.3

and dented cars P(C) =0.4

as these process seems to be independent,

hence probability of rejection=P(EUC) =P(E)+P(C) -P(EnC =0.3+0.4-0.3*0.4 =0.58

b)part (i)P(E1UC)=P(E1)+P(C) -P(E1nC) =0.1+0.4-0.1*0.4 =0.46

part (ii)P(E1UE2UC) =P(EUC) as from above E1 and E are disjoint sets and are part of E

=0.3+0.4-0.3*0.4 =0.58

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