A) \[4/11\]
B) \[3/11\]
C) \[4/13\]
D) \[3/13\]
Correct Answer: C
Solution :
[c] Let A, B and C be the events that the transistor chosen is manufactured by the companies A, B and C, respectively. Let E be the event that the transistor is of excellent quality. So, \[P(A)=\frac{18}{50};\,\,\,\,P(B)=\frac{20}{50};\,\,\,\,P(C)=\frac{12}{50}\] Also, \[P(E/A)=0.9;\] \[P(E/B)=0.6;\] \[P(E/C)=0.9\] \[\therefore \,\,\,\,\,P(E)=P(A)\,\,P(E/A)+P(B)\,\,P(E/B)+P(C)\,\,P(E/C)\] \[=\frac{39}{50}\] \[\therefore \] Required probability \[=P(B/E)\] \[=\frac{P(B)\,P(E/B)}{P(E)}=\frac{\frac{20}{50}\times 0.6}{\frac{39}{50}}=\frac{4}{13}\]You need to login to perform this action.
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