Sampling¶
penguin eating ice cream. Style by August Macke. Created with stablediffusionweb.com
Exercise 1: Ice Cream¶
In the summer, penguins like ice cream. Every penguin has their own individual taste. Let’s consider three penguins:
Ada likes to have one scoop of each type available. She refuses to eat ice cream with fewer scoops. The order of the scoops matters, so mango-vanilla is not the same as vanilla-mango.
Bashir likes to have 2, 3 or 4 scoops. The order does not matter, but every type of ice cream must occur only once.
Choi has a taste very similar to Bashir, but a type of ice cream may occur multiple times.
Dob has a taste very similar to Choi, but the order of the scoops matters.
Create a table showing how many different ice cream cones one could build for each penguin. Consider the following cases:
2 types of ice cream and 2 scoops
3 types of ice cream and 2 scoops
3 types of ice cream and 3 scoops
4 types of ice cream and 2 scoops
4 types of ice cream and 3 scoops
Exercise 2: Ice Cream Deluxe¶
The penguins have found an ice cream shop that offers 32 different types of ice cream. Bashir seizes the opportunity and orders an ice cream with 7 scoops. How many friends should he invite to try all possible combinations?
penguin eating ice cream. Style by Miro. Created with stablediffusionweb.com
Exercise 3: Ice Cream Factory¶
The penguins have found the ice cream factory. The factory continuously produces ice cream scoops and puts them on a conveyor belt.
One in ten scoops is a mango ice cream scoop. Choi grabs 10 scoops at random. What is the probability that they have exactly 3 mango scoops?
Exercise 4: Packaging¶
The scoops are packaged into boxes of 100 scoops. What is the probability that a box will contain exactly 15 mango scoops?
Optional: What is the probability that a box contains 5 scoops or less?