0. Solve the questions on this page?

[2] When you roll a dice, determine the event and the corresponding probability of that event.

a. Sample space S. = { } P(S) =

b. A = {even number} ={ } P(A) =

c. B = {number less than or equal to 4} = { } P(B) =

d. A and B = { } P(A and B) =

e. A or B= { } P(A or B) =

f. Specify the data for (A and BC), (A and B), ( AC and B), (AC and BC) in the right Venn Diagram. Verify the addition rule to compute P(A or B) = P(A) + P(B) - P(A and B) =

2. [4.5] Three airlines serve in Moncton. American Airlines (AA) has 20% of all the scheduled flights, British Airline (AB) has 10%, and Air Canada (AC) has the remaining 70%. Their on-time departure rates are 80%, 50%, and 90% respectively. We do not consider the joint operation.

Let's define the event as follows: Airline(A) - A1: AA, A2: AB, A3: AC; On-time (B) - B1: On-time, B2: Not on-time

a.[1] Use the following contingency tables to compute the conditional probability, the joint probability & the resulting Bayesian probability.

b. [3] What's the probability that [Answer with the closest TWO decimal-point number.] the plane selected at random is either AB or AC?

both of them were AB, if we picked two planes at random?

the plane selected at random is AA and arrives on-time?

the plane selected at random is AC or arrives on-time?

a plane just arriving on time was AB? a plane arriving 15 minutes after the schedule was airline AA?

c. [0.5] Are the event of AC and event of arriving on-time independent?

3. [3.5] Facebook reports that 70% of their users are based on a mobile platform (say, "mobile users"), and that 80% of their users log on to Facebook every day. Suppose that 55% are mobile users who log on every day.

a. [1.5] Construct the contingency table:

b. [2] What % of Facebook's users are mobile users? What type of probability is the "20%" mentioned in the table? What is the probability that one is a mobile user, if one logs on every day? Are "the mobile users" and "Log on Every Day" independent? (Show your reasons!)