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?
Accepted Solution
A:
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 be0.85(0.85) = 0.7225 = 72.25%.The probability that 9 cheeses chosen at random will all be pasteurized will be0.85⁹ = 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 be1-0.2316 = 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.