Probability: Is there a difference in the way these questions are phrased
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Probability: Is there a difference in the way these questions are phrased

[From: ] [author: ] [Date: 11-09-16] [Hit: ]
-They will be the same thing. Perhaps they are asking you to do it two different ways, though I dont see how the rephrasing alters the question. Both are asking the probability of the event: exactly 3 of the first 14 use credit, and then the 15th uses credit.You can use the negative binomial,......
Paul works at a gas station. He knows that 40% of all customers who purchase gas pay at the pump with a credit card. Assume that customers either pay at the pump with a credit card or not independently of each other.

1.) What is the probability that the fourth customer to pay at the pump with a credit card is the fifteenth customer purchasing gas?

2.) What is the probability that the fifteenth customer purchasing gas is the fourth one to pay at the pump with a credit card?

Are the questions asking the same thing? Are they both solvable using a negative binomial distribution?

Thanks.

-
They will be the same thing. Perhaps they are asking you to do it two different ways, though I don't see how the rephrasing alters the question. Both are asking the probability of the event: exactly 3 of the first 14 use credit, and then the 15th uses credit.

You can use the negative binomial, though I like to do it this way:

= p(3 of the first 14 use credit) * p(15th uses credit)
= C(14,3) 0.4^3 0.6^11 * 0.4
1
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