Pre-Lab Exercise: A random experiment consists of rolling two dice-a red die and

Question

Pre-Lab Exercise: A random experiment consists of rolling two dice-a red die and a blue die. Consider the following events: A: the uppermost faces sum to an odd number, B: At least one of the uppermost faces shows a 1'.Put a A and or a B in the table below where each outcome is possible. The Outcome of the Red Die List the elements in A. Use the format (Red, Blue) for example (G, 2) refers to the (a) (b) (c) instance red die 3 and the blue die - 2. List the elements in B. List the elements in... O (A n B) () (A u B). (d) Explain, in your own words, what the events mentioned in () represent e) What does A represent? How many ways can AC occur, n(A? () Is it impossible for A and B to happen simultaneously/mutually exclusive? Why or why not? Explain, by considering the possibility of both events occurring. possibility, as in (f). In your own words what does this event represent? think of wording this that mean the same thing? Find the number of ways this can (g) Are the events AC and B mutually exclusive? Why or why not? Explain, again using (h) In your own words what does (A n B) represent? Are there any other ways you can happen, n(A n B).

Explanation / Answer

Solution:-

Sample space = {(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)}

a). Sum is odd, A = {(1,2)(1,4)(1,6)(2,1)(2,3)(2,5)(3,2)(3,4)(3,6)(4,1)(4,3)(4,5)(5,2)(5,4)(5,6)(6,1)(6,3)(6,5)}.

b). At least one face is "1", B = {(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)(2,1)(3,1)(4,1)(5,1)(6,1)}.

c). (i) (A and B) = {(1,2)(1,4)(1,6)(6,1)}

(ii) (A or B) = {(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)(2,1)(2,3)(2,5)(3,1)(3,2)(3,4)(3,6)(4,1)(4,3)(4,5)(5,1)(5,2)(5,4)(5,6)(6,1) (6,3)(6,5)}.

d). The events in part (i) i.e., (A and B) represents set of those events that have occured in both the events A as well as in B. Thus, we write only those which are there in event A as well as in event B.

In part (ii) i.e., (A or B) represents all those events that have occured either in A or in B.

e). Ac are all those events, where the numbers on the dice adds up to an even number.

f). No, it is not impossible for A and B, to happen simultaneously, as sample space of (A and B) is not a null set.

g). No, they are not mutually exclusive.

h). (Ac and B) = {(1,1)(1,3)(1,5)(3,1)(5,1)}.

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