Respuesta :
Answer:
The probability that the sixth customer buys sour milk is [tex]\frac{1}{5}[/tex].
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)
= [tex]P(2\ sour\ cartons)=\frac{2}{5}[/tex]
- 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)
= [tex]P(1\ sour\ cartons)=\frac{1}{5}[/tex]
- 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)
= [tex]P(0\ sour\ cartons)=\frac{0}{5}[/tex]
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)
[tex]=\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}[/tex]
Thus, the probability that the sixth customer buys sour milk is [tex]\frac{1}{5}[/tex].
