Let’s count. Counting sequences

Do your best in trying to solve the following problems. It is normal that this step will take some time, we recommend to perseverate and wait before looking at the complete solution of the exercises in the video or in the pdf below.

Exercise 1. Consider an urn containing 10 red balls and 4 black ones. We draw three balls. Determine the probability that:

• The first ball extracted is Red;

• The third ball extracted is Red.

Exercise 2: Birthday’s problem. What is the probability that two (or more) people randomly chosen from a group of 25 people have the same birthday?

Hint: Compute the probability of the complementary event.