Machines A, B and C make resistors 1, 2 and 3 respectively. The acceptability of the three resistors are 90%, 93% and 81% respectively. Three resistors arepicked at random sampling with replacement. Find the probability that i. All resistors are acceptable.

 

b.      Machines A, B and C make resistors 1, 2 and 3 respectively. The acceptability of the three resistors are 90%, 93% and 81% respectively. Three resistors arepicked at random sampling with replacement. Find the probability that

 

i.                    All resistors are acceptable.                                                                           

ii.           P(A) = 0.9

 

iii.         P(B) = 0.93

 

iv.         P(C) = 0.81

 

Since A , B and C are the independent events, therefore

P(AՌBՌC) = P(A) P(B) P(C)

                  

                = 0.9 * 0.93 * 0.81

                    = 0.678

                    = 67.8%  Answer

 

v.                  All resistors are not acceptable.

                                                                       

P(all resistors are not acceptable)   =   1 -  P(all resistors are acceptable)

                                                      = 1 – 0.678

                                                      = 0.322

                                                      = 32.2%   Answer

 

 

 

vi.                At least one resistor is acceptable.                                                                [Marks-01]

 

P(At least one resistor is acceptable) = P(AUBUC)

P(AUBUC) = P(A) +P(B) +P(C) -P(AՌB)-P(BՌC) – P(AՌC) + P(AՌBՌC)

                  

 = 0.9 + 0.93 +0.81 – 0.9*0.93 – 0.93*0.81 – 0.9*0.81 + 0.678

              

     = 0.998

                 

   = 99.8%  Answer