Answer:
0.4198 = 41.98% probability that he or she has a basic model
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: Extended warranty
Event B: Basic model
Probability of extended warranty:
34% of 50%(basic model)
47% of 100 - 50 = 50%(deluxe model). So
[tex]P(A) = 0.34*0.5 + 0.47*0.5 = 0.405[/tex]
Intersection of events A and B:
34% of 50%(basic model with extended warranty). So
[tex]P(A \cap B) = 0.34*0.5 = 0.17[/tex]
How likely is it that he or she has a basic model
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.17}{0.405} = 0.4198[/tex]
0.4198 = 41.98% probability that he or she has a basic model
