Question

A batch of 580 containers for frozen orange juice contains 8 that are defective. Two are selected, at random, without replacement from the batch.
a) What is the probability that the second one selected is defective given that the first one was defective?
b. What is the probability that both are defective?
c. What is the probability that both are acceptable? Three containers are selected, at random, without replacement, from the batch.
d. What is the probability that the third one selected is defective given that the first and second ones selected were defective?
e. What is the probability that the third one selected is defective given that the first one selected was defective and the second one selected was okay?
f. What is the probability that all three are defective?

Answer 1

Answer:

a. 0.12109

b. 0.0001668

c .0.9726

d. 0.01038

e. 0.01211

f. 0.000001731

Step-by-step explanation:

Sample size = 580

Defective units = 8

Number of picks = 2

a) If the first container is defective, there 7 defective containers left in a population of 579. The probability of selecting a defective one is:

$P=\frac{7}{579}=0.121$

b) The probability that both are defective is given by:

$P=\frac{8}{580}*\frac{7}{579}= 0.000167$

c) The probability that both are acceptable is given by:

$P=\frac{580-8}{580}*\frac{579-8}{579}= 0.9726$

d) In this case, two defective units were removed from the batch, the probability that the third is also defective is:

$P=\frac{6}{578}}= 0.0104$

e) In this case, one acceptable and one defective unit were removed from the batch, the probability that the third is also defective is:

$P=\frac{7}{578}= 0.01211$

f) The probability that all three are defective is given by:

$P=\frac{8}{580}*\frac{7}{579}*\frac{6}{578} = 0.000001731$