contestada

All bags entering a research facility are screened. Ninety-seven percent of the bags that contain forbidden material trigger an alarm. Fifteen percent of the bags that do not contain forbidden material also trigger the alarm. If 1 out of every 1,000 bags entering the building contains forbidden material, what is the probability that a bag that triggers the alarm will actually contain forbidden material?

Respuesta :

pedrocarratore

Answer:

0.00643

Step-by-step explanation:

The probability of a bag triggering the alarm is given by the probability of the bag containing forbidden material and triggering the alarm plus the  probability of the bag NOT containing forbidden material and triggering the alarm:

[tex]P(T) = \frac{1}{1,000}*0.97 + \frac{999}{1,000}*0.15\\P(T) = 0.15082[/tex]

The probability that a bag that has triggered the alarm contains forbidden material is:

[tex]P(F)=\frac{\frac{1}{1,000}*0.97}{P(T)} =\frac{\frac{1}{1,000}*0.97}{0.15082}\\P(F)=0.00643[/tex]

Otras preguntas