1 Answer

Kdojeteri · Answer 1 · 2021-03-10T02:33:32+0000

Answer:

The probability of the event that each of the 18 customers are able to purchases their desired drink is = 0.4653.

Explanation:

Given that,

Only regular Coke and diet Coke is dispensed a soft-drink machine .

Diet drink that purchases from this machine is 70% of all purchases.

There are total 18 customers, and X represents number of customer who choose diet coke and Y represents number of customer who choose regular coke.

There are only 12 cans of each types available and X+Y= 18.

The combination of (X,Y) are

(12,6),(11,7),(10,8),(9,9),(8,10),(7,11),(6,12)

The number of diet coke varies 6 to 12

The random variable X follows the binomial distribution of n=18 and p=70%=0.70

$b(x;n,p)=\left(\begin{array}{c}n\\x\end{array}\right) p^x(1-p)^(n-x)$

The probability that each customers get theirs favorable drink is

=P(6≤X≤12)

=P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)+P(X=11)+P(X=12)

$P(X=6)=\left(\begin{array}{c}18\\6\end{array}\right) (0.70)^6(1-0.70)^(18-6)$

=0.00116

$P(X=7)=\left(\begin{array}{c}18\\7\end{array}\right) (0.70)^7(1-0.70)^(18-7)$

=0.00464

$P(X=8)=\left(\begin{array}{c}18\\8\end{array}\right) (0.70)^8(1-0.70)^(18-8)$

=0.0149

$P(X=9)=\left(\begin{array}{c}18\\9\end{array}\right) (0.70)^9(1-0.70)^(18-9)$

=0.0386

$P(X=10)=\left(\begin{array}{c}18\\10\end{array}\right) (0.70)^(10)(1-0.70)^(18-10)$

=0.0811

$P(X=11)=\left(\begin{array}{c}18\\11\end{array}\right) (0.70)^(11)(1-0.70)^(18-11)$

=0.1376

$P(X=12)=\left(\begin{array}{c}18\\12\end{array}\right) (0.70)^(12)(1-0.70)^(18-12)$

=0.1873

∴P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)+P(X=11)+P(X=12)

=0.4653

The probability that each of the 18 is able to purchases the type of drink desired is = 0.4653.

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