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Suppose a batch of widgets has a 50% prior probability of coming from supplier 1; otherwise it comes from supplier 2. Suppose 3% of supplier 1’s widgets are defective and 2% of supplier 2’s widgets are defective (independently). Ten widgets from the batch are tested.

a. What is the probability the first widget is defective?
b. What is the probability the second widget is defective?
c. What is the probability the second widget is defective given the first is defective?
d. What is the probability that the first widget is defective given the 10th widget is defective?
e. What is the probability the first widget is defective if we know it came from supplier 1?
f. What is the probability the second widget is defective if the first is defective and we know the batch came from supplier 1?
g. What are the posterior odds the batch came from supplier 1 given two widgets are tested and found defective?
h. What is the posterior probability (write the expression) that the batch is from supplier 1 if all ten widgets aredefective?

Respuesta :

TomShelby

Answer:

a) 2.5%

b) 2.5%

c) 0.0625%

d) 0.0625%

e) 3%

f) 0.09%

Step-by-step explanation:

for a and b we are considering the probabilities of a single widget so they are the same:

0.03 x 50% + 0.02 x 50% = 0.015 + 0.01 = 0.025 = 2.5%

c) then we have two defective widget in a row:

0.025 x 0.025 = 0.000625 = 0.0625%

d) we have the same situation given a fixed probbility (10th is defenctive) we add another which 1st begin defective as well

e) we use only supplier 1

0.03

f) 0.03 x 0.03 = 0.0009 = 0.09%