A cheese can be classified as either raw dash milk or pasteurized. Suppose that 89​% of cheeses are classified as pasteurized. Two cheeses are chosen at random. What is the probability that both cheeses are pasteurized​? 

Given that 89% of cheeses are classified as pasteurized, we want to calculate the probability that both cheeses chosen at random are pasteurized.

Let's define the probability that a cheese is pasteurized as \( P(\text{Pasteurized}) = 0.89 \).

Since we are selecting two cheeses at random and the selection is independent, the probability that both cheeses are pasteurized is:

\[
P(\text{Both Pasteurized}) = P(\text{First Pasteurized}) \times P(\text{Second Pasteurized}) = 0.89 \times 0.89 = 0.89^2
\]

Now, calculating \( 0.89^2 \):

\[
0.89^2 = 0.7921
\]

So, the probability that both cheeses are pasteurized is approximately **0.7921**, or **79.21%**.

Would you like further details or have any questions?

Here are some related questions:
1. What is the probability that neither cheese is pasteurized?
2. How would the result change if the cheeses were not chosen independently?
3. What is the probability that exactly one cheese is pasteurized?
4. If three cheeses were chosen, what is the probability that all three are pasteurized?
5. What is the complementary probability that at least one cheese is not pasteurized?

**Tip:** In independent probability problems, always multiply the individual probabilities of each event occurring.

A cheese can be classified as either raw milk or pasteurized. Suppose that 89% of cheeses are classified as pasteurized. Two cheeses are chosen at random. What is the probability that both cheeses are pasteurized?

Learn how to calculate the probability of selecting two pasteurized cheeses at random, given that 89% of cheeses are classified as pasteurized. This problem involves the multiplication rule for independent events and is suitable for students in Grades 8-10.

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