Question

This past spring, Nintendo released a video game titled Animal Crossing. One of the things you can do in this game is dig for fossils and put them in a museum. There are 73 possible fossils to find. Every day, random fossils will appear on the island. The fossils that appear can repeat (either on the same day or different days). Currently I have found 70 of the fossils.

1) What is the probability that I find a new fossil on the next day I play?

2) What is the probability that I find at least one new fossil in the next 7 days I play?

3) How many days would I expect before I find a new fossil?

4) How many days would I expect before I find all the remaining fossils? (It's fair to assume that I find no more than 1 new fossil in a given day.

Another thing you can do in Animal Crossing game is shake trees to see if they will drop anything. Each day, 2 trees will drop items, while 3 different trees will drop wasps; trees cannot have both an item and a wasp. My island has 20 trees.

5) What is the probability that I find all 3 wasps in the first 10 trees I shake?.

6) What is the probability that I find both items before I find all 3 wasps?

Answer 1