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.
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.
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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
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