Question

A cheese can be classified as either raw-milk or pasteurized. 82% of cheeses are classified as pasteurized.

a. Two cheeses are chosen at random. What is the probability that both cheeses are pasteurized?
b. Four cheeses are chosen at random. What is the probability that all four cheeses are pasteurized?
c. What is the probability that at least one of four randomly selected cheeses is raw-milk? Would it be unusual that at least one of four randomly selected cheeses is raw-milk?

Answer 1

Explanation:

A cheese is said to be classified as either raw-milk or pasteurized.

Given that: 82% is pasteurized,

Then:

Supposed two cheeses are chosen at random;

P(both cheeses are pasteurized) = 0.82 × 0.82

= 0.6724

If four cheeses are chosen at random;

P(that all four cheeses are pasteurized) = 0.82 × 0.82 × 0.82 × 0.82

P(that all four cheeses are pasteurized) = 0.452

The required probability for at least one of the four randomly selected cheeses is raw milk is:

P(at least one of the randomly selected cheese is raw milk) = 1 - P(that all four cheeses are pasteurized)

P(at least one of the randomly selected cheese is raw milk) = 1 - 0.452

P(at least one of the randomly selected cheese is raw milk) = 0.548

However, since the probability that at least one of the randomly selected cheese is raw milk is greater than one; then we can conclude that;

It is not unusual that at least one of four randomly selected cheeses is raw-milk.