Problem No. 4. _10ps. Given A lot of 1120 components contains 255 that are defec

Question

Problem No. 4. _10ps. Given A lot of 1120 components contains 255 that are defective Two components are drawn at random and tested Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective (1) Find P(A) (2) Find P(BA) (3) Find P(AnB) (4) Find PlanB) (5) Find P(B) (6) Find P(AIB) (7) Are A and B independent? Is it reasonable to treat A and B as though they were independent? Explain Round numerical answers to the fourth decimal place.

Explanation / Answer

1)P(A) =255/1120 =0.2277

2)P(B|A) =254/1119=0.2270

3)P(An B) =P(A)*P(B|A) =(255/1120 )*(254/1119)=0.05168

4)P(AcnB) =P(Ac)*P(Ac|B)=(1-255/1120)*(255/1119)=0.1760

5) P(B) =P(An B)+P(AcnB) =0.2277

6)P(A|B) =P(A n B)/P(B) =0.2270

7)as P(A|B) is not equal to P(A) ; therefore A and B are not independent.

we can consider above as independent as sample size n=2 and total population size N =1120

hence n/N <=0.05

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