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An owner of a small store knows that in the last week 54 customers paid with cash, 42 paid with a debit card, and 153 paid with a credit card. Based on the number of customers from last week, which fraction is closest to the probability that the next customer will pay with cash?



Answer :

asufan4ever
You would add 54+42+153=249 to find the total amount of customers from the previous week. Then you would divide 54/249= 0.2168 to find the amount of customers that used cash to total customers. The closest fraction would be about 1/5. 

Based on the number of customers from last week, the fraction is closest to the probability that the next customer will pay with cash is 54/249

How to get population mean?

Suppose population is wide and you cannot evaluate all the population at once. Then you do sampling of large enough size randomly. The mean of that sample will be then the estimate for the mean that population will pertain.

What is experimental probability?

Experimental probability calculates the probability of some event from the results of experiments.

For an event E, we get the experimental probability of that event

[tex]P_e(E) = \dfrac{\text{Number of times E occurred}}{\text{Number of times experiments was done}}[/tex]

where, [tex]P_e(E)[/tex] is denoting experimental probability of occurrence of E.

Here, the customers are not all known to us, they are population.

But we have some data of the previous customer. Taking them as the sample, we have:

Experimental probability of an event from sample = Predicted probability for that event in population.

For this case, from the previous data, we have:

  • 54 customers paid with cash
  • 42 customers paid with debit card
  • 153 customers paid with a credit card.

Total customers who paid = 153 + 42 + 54 = 249

Total customers who paid with cash = 54

Thus, if we take:

E = event that a customer pays with cash, then:

[tex]P_e(E) = \dfrac{54}{249}[/tex]

This is the probability deduced from the previous data that the next customer will pay with cash.

Thus, based on the number of customers from last week, the fraction is closest to the probability that the next customer will pay with cash is 54/249

Learn more about probability here:

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