Question

If a restaurant purchases organic food there is a 66% chance it will go bankrupt. If a restaurant does not purchase organic food there is a 64% chance it will go bankrupt. Only 12% of businesses purchase organic food. When a restaurant goes bankrupt what is the probability it purchased organic food

Answer 1

0.1233 = 12.33% probability it purchased organic food

Explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

`P(B|A) = (P(A \cap B))/(P(A))`

In which

P(B|A) is the probability of event B happening, given that A happened.

`P(A \cap B)` 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

`P(A) = 0.66*0.12 + 0.64*0.88 = 0.6424`

Intersection of A and B:

Bankrupt when purchases organic food. So

66% of 12%

`P(A \cap B) = 0.66*0.12 = 0.0792`

When a restaurant goes bankrupt what is the probability it purchased organic food

`P(B|A) = (P(A \cap B))/(P(A)) = (0.0792)/(0.6424) = 0.1233`

0.1233 = 12.33% probability it purchased organic food