Question

In one online store, 8\%8%8, percent of the orders are placed by new customers. Let NNN be the number of orders placed in a day to reach the stores first new customer. Assume each order's customer status is independent. Find the probability that the first new customer places the 5^{\text{th}}5 th 5, start superscript, start text, t, h, end text, end superscript order of the day. You may round your answer to the nearest hundredth. P(N

Answer 1

Rounding to the nearest hundredth, 0.06 = 6% probability that the first new customer places the 5th order.

Explanation:

We want to find that the first order placed by a new customer is the 5th.

We have that:

8% = 0.08 probability that an order is placed by a new customer.

1 - 0.08 = 0.92 = 92% probability that an order is placed by an old customer.

Probability that the first order placed by a new customer is the 5th:

First four all old, each with 0.92 probability.

Firth new, with 0.08 probability. So

`P = (0.92)^4*0.08 = 0.0573`

Rounding to the nearest hundredth, 0.06 = 6% probability that the first new customer places the 5th order.