1. Prove De Morgan's laws: Let A, B X. Show:

(a) X\(A B) = (X\A) (X\B).

(b) X\(A B) = (X\A) (X\A).

 

2. A box has 4 coins in it. One is red on both sides, one is blue on both sides, and two are red on one side and blue on the other. A coin is drawn from the box and you see it  is red. What is the probability that the other side of the coin is red?

 

 

3. Consider a six-sided dice numbered from one to six. Let's call realization the number returned by rolling the dice. What is the expected sum of the realizations of 10 dice throws? Out of these 10 dice throws what is the probability of observing at least three realizations of the number six? What is the probability of observing exactly three realizations of the number six?