Answer:
54% probability that a person likes Italian food, but not Chinese food.
82% probaility that a person likes at least one of these foods
79% proability that a person likes at most one of these foods
Step-by-step explanation:
We solve this problem building the Venn's diagram of these probabilities.
I am going to say that:
A is the probability that a person likes Italian food.
B is the probability that a person likes Chinese food.
We have that:
In which a is the probability that a person likes Italian food but not Chinese and is the probability that a person likes both Italian and Chinese food.
By the same logic, we have that:
The probability that a person likes both foods is 0.21.
This means that
The probability that a person likes Chinese food is 0.28
This means that
So
The probability that a person likes Italian food is 0.75
This means that
So
Determine the probability that a person likes Italian, but not Chinese
This is a.
54% probability that a person likes Italian food, but not Chinese food.
Determine the probaility that a person likes at least one of these foods
82% probaility that a person likes at least one of these foods
Determine the proability that a person likes at most one of these foods
Either a person likes at most one of these foods, or it likes both. The sum of the probabilities of these events is decimal 1.
0.21 probability it likes both.
Then
0.21 + p = 1
p = 0.79
79% proability that a person likes at most one of these foods