Exercise 4.8 marks) NOTE: venn diagrams may help you with some parts of this que

Question

Exercise 4.8 marks) NOTE: venn diagrams may help you with some parts of this question. A lot of 1000 components contains 300 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. (a) Find P(A). b) Find P(B| A). (c) Find P(AnB) (d) Find.P(4%2). (e) Eind. P(B). (f) Find P(AB) (g) Are A and B independent? is it reasonable to treat A and B as though they were independent? Explain.

Explanation / Answer

a) P(A) =P(first component is defective) =300/1000 =3/10=0.3 (as there are 300 defective out of 1000)

b)P(B|A) =P(second component id defective given first is defective)=299/999=0.2993 (as there remains 299 defective out of 999 total components if first is defective)

c) P(AnB) =P(first is defective and scond is defective)=(300/1000)*(299/999)=299/3330=0.0898

d) P(AcnB) =P(first is not defective and second is defective) =(700/1000)*(300/999)=70/333=0.210

e) P(B) =P(AnB)+P(AcnB) =(299/3330)+(70/333)=999/3330 =3/10 =0.3

f) P(A|B)=P(AnB)/P(B) =(299/3330)/(3/10) =299/999=0.2993

g) as P(AnB) is not equal to P(A)*P(B) ; therefore A and B are not independent,

However as sample size is large enough; therefore we may assume that events are independent.

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.