Respuesta :
Answer:
0.6603 = 66.03% probability that it will be sent with the ABC Speedy Delivery Company and arrive on time.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Sent by ABC Speedy Delivery Service.
Event B: Arrived on time.
The probability that any given parcel will be sent by the ABC Speedy Delivery Service is 0.71.
This means that [tex]P(A) = 0.71[/tex]
The probability that the parcel will arrive on time given the ABC Speedy Delivery Company was used is 0.93.
This means that [tex]P(B|A) = 0.93[/tex]
Find the probability that it will be sent with the ABC Speedy Delivery Company and arrive on time.
This is [tex]P(A \cap B)[/tex]. So
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]P(A \cap B) = P(B|A)*P(A) = 0.93*0.71 = 0.6603[/tex]
0.6603 = 66.03% probability that it will be sent with the ABC Speedy Delivery Company and arrive on time.
