Answer:
53.85% probability the text books were shipped by truck
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: Textbooks lost.
Event B: Shipped by truck.
40% of the packages sent by truck.
This means that [tex]P(B) = 0.4[/tex]
3.5 percent of the packages carried by truck have been lost.
This means that [tex]P(A|B) = 0.035[/tex]
Probability package is lost:
60% probability it is sent by rail. Of those, 2% are lost.
40% sent by truck. Of those, 3.5% are lost.
So
[tex]P(A) = 0.6*0.02 + 0.4*0.035 = 0.026[/tex]
What is the probability the text books were shipped by truck
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)} = \frac{0.4*0.035}{0.026} = 0.5385[/tex]
53.85% probability the text books were shipped by truck
