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yasarhan2
09.10.2019 •
Mathematics
At tech express, 40% of the customers purchases small coffee and 60% purchases medium. of those customers purchasing small coffee, 30% prefer decaf. of those purchasing medium coffee, 50% prefer decaf.
(a) what is the probability that the next customer will request medium and decaf coffee?
(b) what is the probability that the next customer prefers decaf?
(c) if the next customer prefers decaf, what is the probability that small is requested?
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Ответ:
Answer and explanation:
Given : At Tech Express, 40% of the customers purchases small coffee and 60% purchases medium. Of those customers purchasing small coffee, 30% prefer decaf. Of those purchasing medium coffee, 50% prefer decaf.
Let
customer purchase small coffee.
i.e.![P(A_1)=40\%=0.4](/tpl/images/0303/9600/2c1d6.png)
i.e.![P(A_2)=60\%=0.6](/tpl/images/0303/9600/252d1.png)
Let B be the customer purchase prefer decaf.
So,![P(B|A_1)=30\%=0.3](/tpl/images/0303/9600/36e07.png)
(a) What is the probability that the next customer will request medium and decaf coffee?
i.e.![P(A_2\cap B)=P(A_2)\times P(B|A_2)](/tpl/images/0303/9600/f90b7.png)
(b) What is the probability that the next customer prefers decaf?
i.e.![P(B)=P(A_1\cap B)+P(A_2\cap B)](/tpl/images/0303/9600/f2f95.png)
(c) If the next customer prefers decaf, what is the probability that small is requested?
i.e.![P(A_1|B)=\frac{P(A_1\cap B)}{P(B)}](/tpl/images/0303/9600/6256a.png)
Ответ: