Answer:
33% probability that he or she has a basic model
Step-by-step explanation:
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: Has an extended warranty
Event B: Basic model
Probability of an extended warranty:
48% of 33%(basic model)
48% of 100 - 33 = 67%(deluxe model).
So
[tex]P(A) = 0.48*0.33 + 0.48*0.67 = 0.48[/tex]
Intersection:
48% of 33%(basic model with extended warranty).
So
[tex]P(A \cap B) = 0.48*0.33 = 0.1584[/tex]
How likely is it that he or she has a basic model
[tex]P(B|A) = \frac{0.1584}{0.48} = 0.33[/tex]
33% probability that he or she has a basic model
