Answer:
a) 0.83 = 83% probability that a LED screen will meet specifications.
b) 0.2892 = 28.92% probability that a LED screen that meets specifications was sent by the second supplier.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
![P(B|A) = \frac{P(A \cap B)}{P(A)}](https://tex.z-dn.net/?f=P%28B%7CA%29%20%3D%20%5Cfrac%7BP%28A%20%5Ccap%20B%29%7D%7BP%28A%29%7D)
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
45% from supplier B1, 30% from supplier B2, and the rest from supplier B3.
So 100 - (45 + 30) = 100 - 75 = 25% from supplier B3.
a) Find the probability that a LED screen will meet specifications.
95% of 45%(supplier B1)
80% of 30%(supplier B2)
65% of 25%(supplier B3). So
![p = 0.95*0.45 + 0.8*0.3 + 0.65*0.25 = 0.83](https://tex.z-dn.net/?f=p%20%3D%200.95%2A0.45%20%2B%200.8%2A0.3%20%2B%200.65%2A0.25%20%3D%200.83)
0.83 = 83% probability that a LED screen will meet specifications.
b) Calculate the probability that a LED screen that meets specifications was sent by the second supplier.
Conditional probability.
Event A: Meets specifications.
Event B: Sent by second supplier.
0.83 = 83% probability that a LED screen will meet specifications.
This means that ![P(A) = 0.83](https://tex.z-dn.net/?f=P%28A%29%20%3D%200.83)
Meets specifications and is sent by the second supplier.
80% of 30%, so
![P(A \cap B) = 0.8*0.3 = 0.24](https://tex.z-dn.net/?f=P%28A%20%5Ccap%20B%29%20%3D%200.8%2A0.3%20%3D%200.24)
Probability:
![P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.24}{0.83} = 0.2892](https://tex.z-dn.net/?f=P%28B%7CA%29%20%3D%20%5Cfrac%7BP%28A%20%5Ccap%20B%29%7D%7BP%28A%29%7D%20%3D%20%5Cfrac%7B0.24%7D%7B0.83%7D%20%3D%200.2892)
0.2892 = 28.92% probability that a LED screen that meets specifications was sent by the second supplier.