Respuesta :
Answer:
0.0323 = 3.23% probability that it will not be discovered
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Has emergency locator
Event B: Probability it will not be discovered.
Eighty percent of the light aircraft that disappear while in flight in a certain country are subsequently discovered.
So 20% are not discovered, which means that [tex]P(B) = 0.2[/tex].
90% of the aircraft not discovered do not have such a locator.
So 10% of the aircraft discovered have the location, which means that [tex]P(A|B) = 0.1[/tex]
Probability of having the locator:
75% of 80%(Discovered).
10% of 20%(Not discovered). So
[tex]P(A) = 0.75*0.8 + 0.1*0.2 = 0.62[/tex]
If it has an emergency locator, what is the probability that it will not be discovered?
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)} = \frac{0.2*0.1}{0.62} = 0.0323[/tex]
0.0323 = 3.23% probability that it will not be discovered
