Question

Two different factories both produce a certain automobile part. The probability that a component from the first factory is defective is 2%, and the probability that a component from the second factory is defective is 5%. In a supply of 180 of the parts, 100 were obtained from the first factory and 80 from the second factory.
a. What is the probability that a part chosen at random from the 180 is from the first factory?
b. What is the probability that a part chosen at random from the 180 is from the second factory?
c. What is the probability that a part chosen at random from the 180 is defective?
d. If the chosen part is defective, what is the probability that it came from the first factory?

Answer 1

Answer:

a. 55.56%

b. 44.44%

c. 3.33%

d. 33.33%

Step-by-step explanation:

total supply =  180

a. In the first factory the total number obtained = 100

probability that the chosen part is from the first

= 100/180

= 0.5556

= 55.56%

b. In the second factory total = 80

probability that the chosen part is from the second

= 80/180

= 0.4444

= 44.44%

c. probability that part chosen at random from 180 is defective

= 2% * 0.5556 + 5% * 0.4444

= 0.02*0.5556 + 0.05*0.4444

=  0.011112 + 0.0222

= 0.03331

= 3.33%

d. probability it came rom the first factory if it is defective

$\frac{0.02*0.5556}{0.02*0.5556+0.05*0.4444}$

= $\frac{0.011112}{0.011112+0.0222}$

= $\frac{0.011112}{0.033312}$

= 0.33357

= 33.33%