Question

What is the probability that the manufacturing unit has carbon emission beyond the permissible emission level and the test predicts this? a. 0.2975 b. 0.0525 c. 0.0975 d. 0.5525 e. 0.6325

Answer 1

The conditional probability that the carbon emission is beyond the permissible emission level and the test predicts this is given by:

a. 0.2975.

What is Conditional Probability?

Conditional probability is the probability of one event happening, considering a previous event. The formula is:

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which:

• P(B|A) is the probability of event B happening, given that A happened.

• $P(A \cap B)$ 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:

$P(A) = 0.35, P(B|A) = 0.85$

Then:

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

$0.85 = \frac{P(A \cap B)}{0.35}$

$P(A \cap B) = 0.85(0.35) = 0.2975$

Which means that option a is correct.

More can be learned about conditional probability at brainly.com/question/14398287

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