Solution Found!
A lot of 1000 components contains 300 that are defective.
Chapter 2, Problem 24E(choose chapter or problem)
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 \(P(A \cap B)\).
d. Find \(P\left(A^{c} \cap B\right)\).
e. Find \(P(B)\).
f. Find \(P(A|B)\).
g. Are A and B independent? Is it reasonable to treat A and B as though they were independent? Explain.
Questions & Answers
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 \(P(A \cap B)\).
d. Find \(P\left(A^{c} \cap B\right)\).
e. Find \(P(B)\).
f. Find \(P(A|B)\).
g. Are A and B independent? Is it reasonable to treat A and B as though they were independent? Explain.
ANSWER:Step 1 of 8 :
Given, 300 are defective in a lot of 1000 components. Two components are drawn at random and tested.
Let A be the event that the first component drawn is defective and B be the event that the second component drawn is defective.