Problem 1 (General Addition Rule and Independence): Consider throwing two six sided dice and recording the sum of the two individual die faces. Define the events A, B and C:

Event A: {The sum of the two die faces is an even number}

Event B: {Die 1 equals 5}

Event C: {The sum of the two die equals seven}

a) Compute P(A AND B), P(A AND C), P(B AND C) using the Classical Method.

b) Are any of the events (A, B, and C) disjoint?

c) Compute P(A OR B), P(A OR C), P(B OR C) using the General Addition Rule.

d) Are any of the pairwise events A-B, A-C or B-C independent? i.e. is the Multiplication Rule satisfied?

Problem 2 (Law of Complements):

a) Compute the probability of observing at least one head in a series of eight coin tosses.

b) Compute the probability of observing at least one head in a series of twenty coin tosses.

Problem 3 (Independence): Suppose you go to your neighborhood “RedBox” to select a movie and the “RedBox” is not functioning properly. Instead of selecting the movie of your choice, you will receive two movies at random from a collection of 12 different movies: 4 New Releases, 4 Action Movies, 3 Comedies, and 1 Foreign Films. Define the following events:

A: Event A occurs when one of the two movies you receive is a Foreign Film.

B: Event B occurs when the two movies you receive are from different categories (i.e. New Release and Action).

C: Event C occurs when exactly one of the two movies you receive is an Action Movie.

a) Compute P(A AND B), P(A AND C), P(B AND C) using the Classical Method.

b) Compute P(A OR B), P(A OR C), P(B OR C) using the General Addition Rule.

c) Are any of the pairwise events A-B, A-C or B-C independent? i.e. is the Multiplication Rule satisfied?