Respuesta :
Answer:
0.7407 = 74.07% probability that the customer is a new customer.
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: Pays by credit card
Event B: New customer.
Probability of a customer paying by credit card:
50% of 80%(new customers).
70% of 20%(regular customers). So
[tex]P(A) = 0.5*0.8 + 0.7*0.2 = 0.54[/tex]
Probability of a customer paying by credit card and being a new customer:
50% of 80%, so:
[tex]P(A \cap B) = 0.5*0.8 = 0.4[/tex]
What is the probability that the customer is a new customer?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.4}{0.54} = 0.7407[/tex]
0.7407 = 74.07% probability that the customer is a new customer.
