Respuesta :
Answer:
0.1233 = 12.33% probability it purchased organic food
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: Goes bankrupt
Event B: Purchase organic food.
Probability it goes bankrupt:
66% of 12%(purchases organic food)
64% of 88%(dont purchase organic food).
So
[tex]P(A) = 0.66*0.12 + 0.64*0.88 = 0.6424[/tex]
Intersection of A and B:
Bankrupt when purchases organic food. So
66% of 12%
[tex]P(A \cap B) = 0.66*0.12 = 0.0792[/tex]
When a restaurant goes bankrupt what is the probability it purchased organic food
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0792}{0.6424} = 0.1233[/tex]
0.1233 = 12.33% probability it purchased organic food
