Hello, Please help with the ff problem. Thanks. 7. The table below Visual Inspec

Question

Hello, Please help with the ff problem. Thanks.

7. The table below

Visual Inspection

pass Fail

Pass - - - - - - - -855 - - - - - -95

Fail - - - - - - - - - 10 - - - - - - - - -40

summarizes a population of 1,000 manufactured parts that have been classified according to their visual inspection results and final functional test results: One part is selected at random from the population displayed above. Let V = event that the part passed visual inspection F = event that the part passed final functional test

(a) Calculate P( F )

(b) Calculate P( V )

(c) Calculate P( F and V )

(d) Calculate P( F | V )

(e) Calculate P( V | F)

(f) Calculate P( F | VC) = P( F | V’)

(g) Are the events F and V independent? State why or why not.

Explanation / Answer

a) P(F) = 950/1000 = 0.95

b) P(V) =865/1000 = 0.865

c) P(F and V) =855/1000 = 0.855

d) P(F|V) = P(Fand V)/P(V) = 0.855/0.865 =0.9884

e) P(V|F) =P(F and V) / P(F) = 0.855/0.950 =0.9

f) P(F|V') =P(F and V')/ P(V')

P(V') = 1-P(V) = 1 -0.865 = 0.135

P(F and V') = 95/1000 = 0.095

P(F|V') = 0.095/0.135 =0.7037

g) No , the events are not independent

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