Question

A cheese can be classified as either raw dash milk or pasteurized. suppose that 85​% of cheeses are classified as pasteurized. ​(a) two cheeses are chosen at random. what is the probability that both cheeses are pasteurized​? ​(b) nine cheeses are chosen at random. what is the probability that all nine cheeses are pasteurized​? ​(c) what is the probability that at least one of nine randomly selected cheeses is raw dash milk​? would it be unusual that at least one of nine randomly selected cheeses is raw dash milk​?

Answer 1

​(a) two cheeses are chosen at random. what is the probability that both cheeses are pasteurized​?
P(Both cheeses are pasteurized)​
0.85²=0.7225~72.25%

b]nine cheeses are chosen at random. what is the probability that all nine cheeses are pasteurized​?
 P(9 are pasteurized)
=(0.95)^9
=0.6303
=63.03%

c] what is the probability that at least one of nine randomly selected cheeses is raw dash milk​? would it be unusual that at least one of nine randomly selected cheeses is raw dash milk​?

The event that at least one of the cheese is a raw dash milk is the complement of the event that all of the cheese are pasteurized. The probability of the complement event happening is:
1-the probability of the original event happening
hence:
P(At lease one is a raw dash milk)=1-0.6303=0.3697

So, not only is it not unusual for the raw dash milk to appear given 9 cheeses, it's more likely than not

Answer 2

Answer:

72.25%; 23.16%; 76.84%; No.

Step-by-step explanation:

The probability that any given cheese chosen at random will be pasteurized is 85%, or 0.85.  

This means that the probability of two random cheeses being pasteurized will be

0.85(0.85) = 0.7225 = 72.25%.

The probability that 9 cheeses chosen at random will all be pasteurized will be

0.85⁹ = 0.2316 = 23.16%.

The probability that at least 1 out of 9 cheeses chosen at random will be raw-milk would be the complement of no cheeses being raw milk.  This means all 9 would be pasteurized; we know this probability to be 23.16%.  This means the complement would be

1-0.2316 = 0.7684 = 76.84%.

1 out of 9 cheeses being raw-milk is 1/9 = 0.1111 = 11.11%.

85% of cheese are pasteurized; this means that 100-85 = 15% of cheeses are raw-milk.  Thus an 11% probability would not be unusual.