Mathematics, 09.10.2019 16:30, jellybooooo7446

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?

Answers: 3

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answered: ghernadez

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 A_1 customer purchase small coffee.

i.e. $P(A_1)=40\%=0.4$

A_2 customer purchase medium coffee.

i.e. $P(A_2)=60\%=0.6$

Let B be the customer purchase prefer decaf.

So, $P(B|A_1)=30\%=0.3$

$P(B|A_2)=50\%=0.5$

(a) What is the probability that the next customer will request medium and decaf coffee?

i.e. $P(A_2\cap B)=P(A_2)\times P(B|A_2)$

$P(A_2\cap B)=0.6\times 0.5$

$P(A_2\cap B)=0.3$

(b) What is the probability that the next customer prefers decaf?

i.e. $P(B)=P(A_1\cap B)+P(A_2\cap B)$

$P(B)=P(A_1)\times P(B|A_1)+P(A_2)\times P(B|A_2)$

$P(B)=0.4\times 0.3+0.6\times 0.5$

P(B)=0.12+0.3

P(B)=0.42

i.e. $P(A_1|B)=\frac{P(A_1\cap B)}{P(B)}$

$P(A_1|B)=\frac{0.12}{0.42}$

P(A_1|B)=0.28

answered: Guest

(2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

step-by-step explanation:

simplify the following:

x/x^2 + 3 x + 2 - (x (x + 1))/(x + 2)

combine powers. x/x^2 = x^(1 - 2):

x^(1 - 2) + 3 x + 2 - (x (x + 1))/(x + 2)

1 - 2 = -1:

x^(-1) + 3 x + 2 - (x (x + 1))/(x + 2)

put each term in 1/x + 3 x + 2 - (x (x + 1))/(x + 2) over the common denominator x (x + 2): 1/x + 3 x + 2 - (x (x + 1))/(x + 2) = (x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)):

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2))

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)) = ((x + 2) + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2)):

(2 + x + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

3 x^2 (x + 2) = 3 x^3 + 6 x^2:

(2 + x + 3 x^3 + 6 x^2 + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

2 x (x + 2) = 2 x^2 + 4 x:

(2 + x + 6 x^2 + 3 x^3 + 2 x^2 + 4 x - x^2 (x + 1))/(x (x + 2))

-x^2 (x + 1) = -x^2 - x^3:

(-x^2 - x^3 + 3 x^3 + 6 x^2 + 2 x^2 + 4 x + x + 2)/(x (x + 2))

grouping like terms, 3 x^3 - x^3 + 6 x^2 + 2 x^2 - x^2 + 4 x + x + 2 = (3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2:

((3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

3 x^3 - x^3 = 2 x^3:

(2 x^3 + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

6 x^2 + 2 x^2 - x^2 = 7 x^2: