A soft-drink machine dispenses only regular Coke and diet Coke. Seventy percent of all purchases from this machine are diet drinks. The machine currently has 12 cans of each type. If 18 customers want to purchase drinks before the machine is restocked, what is the probability that each of the 18 is able to purchase the type of drink desired

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

Step-by-step 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

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)

               =0.00116

               =0.00464

              =0.0149

              =0.0386

                =0.0811

                =0.1376

                 =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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