Consider the chance experiment in which the type of transmission—automatic (A) or manual (M)—is recorded for each of the next two cars purchased from a certain dealer. (a) What is the set of all possible outcomes (the sample space)? Sample space = {A, M, AM} Sample space = {AA, AM, MM}     Sample space = {AA, AM, MA, MM} Sample space = {A, M, AA, AM, MA, MM} Sample space = {A, M} (b) Display the possible outcomes in a tree diagram.

The potential outcomes of an experiment consist of the following triples: (a, a, a) (b, b, b) (c, c, c) (a, b, c) (b, c, a) (c, b, a) (a, c, b) (b, a, c) (c, a, b) Assume that every outcome in the sample space is equally likely. Define the following events: A1 = "letter 'a' is in the triple's first position," A2 = "letter 'a' is in the triple's second position," and A3 = "letter 'a' is in the triple's third position." For example, (a, b, c) would be a member of A1, (b, a, c) would be a member of A2, and (c, b, a) would be a member of A3. The events A1, A2, and A3 are not mutually independent. Which of the following statements could be cited in support of this conclusion? Choose from answers below A) Events A1 and A3 are not pairwise independent B) P(A2 ∩ A3) = 1/9 C) Events A1 and A2 are not pairwise independent D) P(A1 ∩ A2 ∩ A3) = 1/9

Naive Approach 1: Say A, B, C are independent ifP (A ∩B ∩C) = P (A)P (B)P (C).Suppose two six-sided dice are tossed and the outcome is noted. Let S denotethe sample space of this experiment.i. Write down the set S explicitly. Consider the eventsA = {(i, i) : i = 1, 2, 3, 4, 5, 6}, B = {(x, y) : 7 ≤x + y ≤10},C = {(x, y) : x + y is 2 or 7 or 8}.Write down the sets A, B, and C explicitly and calculate P (A), P (B), andP (C).

Let S be the sample space from an experiment, and let events A and B have the following properties: A ∩ B = ∅ , and P(A)>0, P(B)>0. With this information select the option that correctly describes the relationship between events A and B? Choose from the options below.    A.) A is independent from B  B.) A is not independent from B  C.) Not enough information to know independence

The sales of a coffee shop in a commercial district is very difficult to predict. The total revenue of the shop can be very good one day and bad the other day. The revenue can be classified into three different categories as High, Medium or Low a) Explain how we can see the revenue of the coffee shop as a "Random Experiment" b) Write down the sample space of this random experiment. c) Write down the event that revenue is high or medium using set notation. Write down a new event that is disjoint (mutually excusive) to the previous event. d) What would be the appropriate observation points (epochs) of the revenue? Explain.

34 Probab 12. A bag contains two red. two yellow, and three blue balls. In an experiment, one ball is drawn from the bag and its color is noted, and then a second half is drawn and its color noted, (i) Draw a tree diagram for this experiment. (ii) How many outcomes are there in the sample space? Gii) What are the outcomes in the event, "two balls of the same color are selected"? tonr Otherwisa the