Respuesta :
Answer:
If a motor is found to be good, there is a 37.87% probability that it came from company B.
Step-by-step explanation:
This can be formulated as the following problem:
What is the probability of B happening, knowing that A has happened.
It can be calculated by the following formula
[tex]P = \frac{P(B).P(A/B)}{P(A)}[/tex]
Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.
For this problem, we have the following question:
What is the probability that the motors comes from company B, given that the motor is good?
P(B) is the probability of the motor coming from company B. Company B supplies 40%, so [tex]P(B) = 0.40[/tex].
P(A/B) is the probability of the motor being good, given that it comes from company B. 20% of the motors from company B are, which means that 80% are good, so [tex]P(A/B) = 0.8[/tex].
P(A) is the probability that the motor is good. Company A supplies 30% of the motors, of which 90% are good. Company B supplies 40% of the motors, of which 80% are good. Company C supplies the rest, that is 100%-(40%+30%) = 30%. Of which 85% are good. So:
[tex]P(A) = 0.3*(0.9) + 0.4*(0.8) + 0.3*(0.85) = 0.845[/tex]
Finally
[tex]P = \frac{P(B).P(A/B)}{P(A)} = \frac{0.8*0.4}{0.845} = 0.3787[/tex]
If a motor is found to be good, there is a 37.87% probability that it came from company B.
