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 ?

(a) two cheeses are chosen at random. what is the probability that both cheeses are pasteurized ?

P (Both cheeses are pasteurized)

0.85 ²=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