The conditional probability that the carbon emission is beyond the permissible emission level and the test predicts this is given by:
a. 0.2975.
<h3>What is Conditional Probability?</h3>
Conditional probability is the probability of one event happening, considering a previous event. The formula 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.
In this problem, we have that the events are as follows:
- Event A: Carbon emission beyond the permissible emission level.
- Event B: Test predicts this.
We have that 35% of the units have carbon emission beyond the permissible emission level, and the test is 85% accurate, hence:
![P(A) = 0.35, P(B|A) = 0.85](https://tex.z-dn.net/?f=P%28A%29%20%3D%200.35%2C%20P%28B%7CA%29%20%3D%200.85)
Then:
![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)
![0.85 = \frac{P(A \cap B)}{0.35}](https://tex.z-dn.net/?f=0.85%20%3D%20%5Cfrac%7BP%28A%20%5Ccap%20B%29%7D%7B0.35%7D)
![P(A \cap B) = 0.85(0.35) = 0.2975](https://tex.z-dn.net/?f=P%28A%20%5Ccap%20B%29%20%3D%200.85%280.35%29%20%3D%200.2975)
Which means that option a is correct.
More can be learned about conditional probability at brainly.com/question/14398287
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Answer:
I do too :(
Step-by-step explanation:
Answer:
hgdss
Step-by-step explanation:
Answer:
5^3
Step-by-step explanation:
5^3 is the index form of 5×5^2