A lot of 10 components contains 3 that are defective. Two components are drawn at random and tested. Let A be the event that that the first component drawn is defective, and B be the event that
The second component drawn is defective. a. Find P(A).
b. Find $P ( B \mid A )$
c. Find P(A and B).
d. Are A and B independent?
A) a. 0.3333
b. 0.1250
c. 0.1000
d. Yes
B) a. 0.3000
b. 0.2222
c. 0.0667
d. Yes
C) a. 0.3000
b. 0.3333
c. 0.1000
d. No
D) a. 0.3000
b. 0.2222
c. 0.0667
d. No

Question

Quizplus · Accepted Answer

P(A) is the probability of drawing a defective component first, which is 3/10 = 0.3000. P(B|A) is the probability of drawing a defective component second given the first was defective, which is 2/9 = 0.2222. P(A and B) is the probability both are defective, which is (3/10)*(2/9) = 0.0667. Events A and B are not independent because P(A and B) ≠ P(A)*P(B).

A Lot of 10 Components Contains 3 That Are Defective P(B∣A)P ( B \mid A )P(B∣A)

A Lot of 10 Components Contains 3 That Are Defective $P ( B \mid A )$