Question

In Animal Crossing (the newly released game for the Nintendo Switch), one of the challenges is to catch 50 fish in a row. Because of randomness in the way the fish nibble, it can be a bit tricky1 . Assume that my long-term average for catching fish is 95%.

1. What is the probability that I catch the next 50 fish in a row, without missing any?

2. How many fish would I expect to catch in a row before I missed one?

3. What is the probability that I catch 45 or fewer of the next 50 fish? (don’t have to be in a row)

4. Out of 50 fish, how many would I expect to catch? (don’t have to be in a row) Also in Animal Crossing (the same newly released video game), one can gather lumber by hitting a tree with an axe. Each tree can be hit 3 times daily, to produce 3 pieces of lumber (1 hit = 1 lumber). The type of lumber created with each hit is uniformly distributed between hardwood, wood, and softwood.

5. If I have 6 trees, what is the probability I will collect at least 5 pieces of hardwood, if I hit all trees the maximum 3 times?

6. What is the probability that a tree hit 3 times produces no softwood at all? Like the trees in the previous problem, bamboo can also be hit with an axe 3 times per day to produce 3 pieces of bamboo2 . Unlike trees, bamboo produces only 2 types of product – young spring bamboo and regular bamboo. Regular bamboo is twice as likely to be dropped as young spring bamboo.

7. On my island, I have a grove of 9 bamboo. How many pieces of young spring bamboo do I expect, if I hit all of them 3 times with an axe?

8. If I want an 80% probability of getting at least 10 pieces of young spring bamboo a day, how many bamboo plants should I have on my island?

Answer 1