A company receives equipment from two factories: 38% from factory A, and all other equipment from factory B. Each factory has a percentage of equipment that is defective: 1% of factory A's equipment is defective, while 4% of factory B's equipment is defective. If a piece of the company's equipment is selected at random, what is the probability that it is defective and from factory B?
A. 0.0248
B. 0.0038
C. 0.6012
D. 0.6600
I already know the answer, I just want to know how to solve it so I know how to handle it on a real exam. It's the only question on my quiz that I struggled with.
It concerns application of the general rule: $$P(E\text{ and }F)=P(E\mid F)P(F)$$where $P(E\mid F)$ denotes the probability of event $E$ under the extra condition that event $F$ occurs.
Application here gives:
$$P(\text{defective and from B})=P(\text{defective}\mid\text{from B})P(\text{from B})=0.04\times0.62=0.0248$$