Applying Probability

Question

The board of directors of a company knows that the probability that the carbon emission from the company’s manufacturing unit is exceeding the permissible level is 35%. A consultant is hired to use a carbon footprint calculator to test for the emission level. The accuracy of this test is said to be 85%.

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 actual polluting is one event .

The testing is a separate, INDEPENDENT event.

To find the probability of BOTH things happening, MULTIPLY their separate probabilities.

P(Emissions being excessive AND The test accurately measuring) =

P(Emissions being excessive) X P(the test being accurate)

0.35 X 0.85 = 0.2975 (Choice A)

I hope this makes sense!