Respuesta :
Answer:
There is a 21.053% probability that this person made a day visit.
There is a 39.474% probability that this person made a one night visit.
There is a 39.474% probability that this person made a two night visit.
Step-by-step explanation:
We have these following percentages
20% select a day visit
50% select a one-night visit
30% select a two-night visit
40% of the day visitors make a purchase
30% of one night visitors make a purchase
50% of two night visitors make a purchase
The first step to solve this problem is finding the probability that a randomly selected visitor makes a purchase. So:
[tex]P = 0.2(0.4) + 0.5(0.3) + 0.3(0.5) = 0.38[/tex]
There is a 38% probability that a randomly selected visitor makes a purchase.
Now, as for the questions, we can formulate them as the following problem:
What is the probability of B happening, knowing that A has happened.
It can be calculated by the following formula
[tex]P = \frac{P(B).P(A/B)}{P(A)}[/tex]
Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.
Suppose a visitor is randomly selected and is found to have made a purchase.
How likely is it that this person made a day visit?
What is the probability that this person made a day visit, given that she made a purchase?
P(B) is the probability that the person made a day visit. So [tex]P(B) = 0.20[/tex]
P(A/B) is the probability that the person who made a day visit made a purchase. So [tex]P(A/B) = 0.4[/tex]
P(A) is the probability that the person made a purchase. So [tex]P(A) = 0.38[/tex]
So
[tex]P = \frac{P(B).P(A/B)}{P(A)} = \frac{0.4*0.2}{0.38} = 0.21053[/tex]
There is a 21.053% probability that this person made a day visit.
How likely is it that this person made a one-night visit?
What is the probability that this person made a one night visit, given that she made a purchase?
P(B) is the probability that the person made a one night visit. So [tex]P(B) = 0.50[/tex]
P(A/B) is the probability that the person who made a one night visit made a purchase. So [tex]P(A/B) = 0.3[/tex]
P(A) is the probability that the person made a purchase. So [tex]P(A) = 0.38[/tex]
So
[tex]P = \frac{P(B).P(A/B)}{P(A)} = \frac{0.5*0.3}{0.38} = 0.39474[/tex]
There is a 39.474% probability that this person made a one night visit.
How likely is it that this person made a two-night visit?
What is the probability that this person made a two night visit, given that she made a purchase?
P(B) is the probability that the person made a two night visit. So [tex]P(B) = 0.30[/tex]
P(A/B) is the probability that the person who made a two night visit made a purchase. So [tex]P(A/B) = 0.5[/tex]
P(A) is the probability that the person made a purchase. So [tex]P(A) = 0.38[/tex]
So
[tex]P = \frac{P(B).P(A/B)}{P(A)} = \frac{0.3*0.5}{0.38} = 0.39474[/tex]
There is a 39.474% probability that this person made a two night visit.
