Question

A small grocery store had 10 cartons of milk, 2 of which were sour. If you are going to buy the 6th carton of milk sold that day at random, find the probability of selecting a carton of sour milk.

Answer 1

Answer:

The probability that the sixth customer buys sour milk is $\frac{1}{5}$.

Step-by-step explanation:

The grocery store has a total of 10 cartons of milk.

The number of cartons of milk that are sour is, 2.

• If none of the sour cartons of milk were bought by the first 5 buyers, then the probability of this event is:

       P (Both the sour cartons are available to be sold to the sixth customer)

        = $P(2\ sour\ cartons)=\frac{2}{5}$

• If only one sour carton of milk is sold to the first 5 buyers then the probability is:

        P (Only one sour cartons is available to be sold to the sixth customer)

            = $P(1\ sour\ cartons)=\frac{1}{5}$

• If both the sour carton of milk is sold to the first 5 buyers then the probability is:

        P (None of the sour cartons is available to be sold to the sixth customer)

         = $P(0\ sour\ cartons)=\frac{0}{5}$

Compute the probability that the sixth customer buys sour milk:

= P (Both sour milk is available for the 6th customer) +  

      P (Only one sour milk is available for the 6th customer) +  

          P (None of the sour milk is available for the 6th customer)

$=\frac{{8\choose 5}{2\choose 0}}{{10\choose 5}} \times\frac{2}{5} +\frac{{8\choose 4}{2\choose 1}}{{10\choose 5}} \times\frac{1}{5} +\frac{{8\choose 3}{2\choose 2}}{{10\choose 5}} \times\frac{0}{5} \\=\frac{56\times2}{252\times5} +\frac{140\times1}{252\times5} +0\\=\frac{1}{5}$

Thus, the probability that the sixth customer buys sour milk is $\frac{1}{5}$.