Question

Detecting traces of TNT.University of Florida researchersin the Department of Materials Science and Engineering have invented a technique to rapidly detect traces of TNT (Today, Spring 2005). The method, which involves shining a laser light on a potentially contaminated object, provides instantaneous results and gives no false positives. In this application, a false positive would occur if the laser light detects traces of TNT when, in fact, no TNT is actually present on the object. Let A be the event that the laser light detects traces of TNT. Let B be the event that the object contains no traces of TNT. The probability of a false positive is 0. Write this probability in terms of A and B using symbols such as$\cup ,\cap$and |.

Short answer

The probability through events of A and B is conditional probability.

$\mathrm{P}\left(\mathrm{A}\right|\mathrm{B})=0$

Step-by-step solution

Important formula

The formula for probability is$\mathbf{P}\mathbf{=}\frac{\mathrm{favourableoutcomes}}{\mathrm{totaloutcomes}}$

The probability in terms of A and B using symbols such as ∪,∩ and |.

Use characters like union, intersection, and conditional probability to express these probability events A and B.

Now, let’s recognize the probability, if a laser light identifies traces of TNT, a false positive will arise in this scenario, if there is no TNT existing on the subject. Let A represents the event in which the laser light identifies traces of TNT and B represent the event in which the items have no traces of TNT.

According to the data, a probability of such a false detection is equivalent to that seen in occurrence A in view of occurrence B.

Thus,our event values are the same, this probability through events of A and B is conditional probability.

Therefore, the probability through events of A and B is conditional probability.

$\mathrm{P}\left(\mathrm{A}\right|\mathrm{B})=0$