Question

2.6-10. in 2016, red rose tea randomly began placing one of ten english porcelain miniature figurines in a l00- bag box of the tea, selecting from ten figurines in the american heritage series. (a) on the average, how many boxes of tea must be purchased by a customer to obtain a complete collection consisting of the ten different figurines? (b) if the customer uses one tea bag per day, how long can a customer expect to take, on the average, to obtain a complete collection?

Answer 1

(a) On average, a customer needs to purchase approximately 23 boxes of Red Rose Tea to obtain a complete collection of the ten different English porcelain miniature figurines.

(b) If the customer uses one tea bag per day, it would take, on average, about 230 days to obtain a complete collection.

Step-by-step explanation:

Red Rose Tea's inclusion of one of ten figurines in each 100-bag box introduces a probability problem involving permutations and combinations. To find the average number of boxes needed for a complete collection, we can use the concept of expected value.

The probability of getting a new figurine in a box decreases with each purchase. The expected value for obtaining the first unique figurine is 10/10, the second is 9/10, and so on. By summing up these probabilities, we find that, on average, a customer needs about 23 boxes to complete the collection.

In terms of time, if a customer uses one tea bag per day, each box provides 100 chances to get a new figurine. Therefore, it takes approximately 23 boxes * 100 days/box = 230 days to collect all ten figurines on average. This calculation assumes a daily tea bag consumption and provides an estimation based on statistical probability. It's important to note that individual experiences may vary, as the process involves randomness and chance.