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Sagot :
Answer:
0.2308 = 23.08% probability that this person made a day visit
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: Visitor made a purchase
Event B: Made a day visit
Probability that a visitor made a purchase:
30% of 20%(day visitors)
10% of 50%(one-night)
50% of 30%(two-night)
So
[tex]P(A) = 0.3*0.2 + 0.1*0.5 + 0.5*0.3 = 0.26[/tex]
Probability of a purchase with a day visit:
30% of 20%. So
[tex]P(A \cap B) = 0.3*0.2 = 0.06[/tex]
How likely is it that this person made a day visit?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.06}{0.26} = 0.2308[/tex]
0.2308 = 23.08% probability that this person made a day visit
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