Question

A cheese can be classified as either raw dash milk or pasteurized. Suppose that 91​% of cheeses are classified as pasteurized. ​(a) Two cheeses are chosen at random. What is the probability that both cheeses are pasteurized​? ​(b) Six cheeses are chosen at random. What is the probability that all six cheeses are pasteurized​? ​(c) What is the probability that at least one of six randomly selected cheeses is raw dash milk​? Would it be unusual that at least one of six randomly selected cheeses is raw dash milk​?

Answer 1

Explanation:

Given that a cheese can be classified as either raw dash milk or pasteurized. Suppose that 91​% of cheeses are classified as pasteurized.

Each cheese is independent of the other and there are only two outcomes.

Hence X = no of cheeses pasteurized is binomial (2,0.91)

a) P(x=2 ) when n=2 is
`(0.91)^2=0.8281`

b) n=6.

P(x=6) =
`(0.91)^6=0.5679`

c) P(atleast one raw dash milk) = 1-P(all pasteurised)

=0.8281

Since probability is 0.83 it is not unusual.