A particular car manufacturer has three factories $F1$, $F2$, $F3$ making $26\%$, $35\%$, and $39\%$, respectively, of its cars. Of their output, $7\%$, $5\%$, and $1\%$, respectively, are defective. A car is chosen at random from the manufacturer’s supply:
What is the probability that the car is defective?
Given that the car is defective, what is the probability that it came from factory F1?
Having a hard time understanding these. Please explain this to me
Best Answer
Hint: Using the law of total probability we have $$ P(\text{defective})=\sum_i P(\text{defective}\mid \text{from }\; F_i)P(\text{from }\; F_i). $$
To find $P(\text{from }\; F_1\mid\text{defective})$ you can use Bayes' theorem since you've just calculated $P(\text{defected})$.