Question

At a coffee shop, 70% of the customers buy a coffee drink, 30% buy food, and 20% buy both a coffee drink and food. Are buying food and buying a coffee drink independent events? How do you know?

Answer 1

Yes.

70% of the customers buy a coffee drink and 30% buy food.

The sum of it is 100% already.

So 20% of it just another addition of information since it cannot exceed 100% of percentage (100% + 20% = 120%).

It also contains a subset for both percentage.

Answer 2

No

Explanation:

If independent,

P(C^F) = P(C) × P(F)

0.2 = 0.3×0.7

0.2 = 0.21 is not a true statement