0,; The Dow Jones average does not rise on the first day but rises on the second day. 0; The Dow Jones average does not rise on either day. and each selects a car. The customers do not know each other, and there is no communication between them. Let the events A and B be defined as follows: A: The customers select at least one Toyota. B: The customers select two cars of the same model. Let events A and B be the following: A: The Dow Jones average rises on the first day. B: The Dow Jones average rises on the second day. a. Show that (AN B) U (ĀNB) = B. b. Show that A U (ĀNB) = AUB. a. Identify all pairs of cars in the sample space. b. Define event A. c. Define event B. d. Define the complement of A. e. Show that (AN B)U(ĀNB) = B. f. Show that A U (ĀOB) = AUB. 3.7 Florin Frenti operates a small, used car lot that has three Mercedes (M, M, M,) and two Toyotas (T, T). Two customers, Cezara and Anda, come to his lot,

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3.6 Consider Example 3.4, with the following four basic
outcomes for the Dow Jones Industrial Average over
two consecutive days:
0;: The Dow Jones average rises on both days.
0; The Dow Jones average rises on the first day
but does not rise on the second day.
0; The Dow Jones average does not rise on the
first day but rises on the second day.
0; The Dow Jones average does not rise on either
day.
Let events A and B be the following:
and each selects a car. The customers do not know
each other, and there is no communication between
them. Let the events A and B be defined as follows:
A: The customers select at least one Toyota.
B: The customers select two cars of the same model.
A: The Dow Jones average rises on the first day.
B: The Dow Jones average rises on the second day.
a. Identify all pairs of cars in the sample space.
b. Define event A.
a. Show that (ANB) U (ĀNB) = B.
b. Show that AU (ĀnB) = AUB.
c. Define event B.
d. Define the complement of A.
e. Show that (AnB) U (ĀNB) = B.
f. Show that A U (ANB) = AUB.
3.7 Florin Frenti operates a small, used car lot that has
three Mercedes (M, M, M,) and two Toyotas (T, T,).
Two customers, Cezara and Anda, come to his lot,
Transcribed Image Text:3.6 Consider Example 3.4, with the following four basic outcomes for the Dow Jones Industrial Average over two consecutive days: 0;: The Dow Jones average rises on both days. 0; The Dow Jones average rises on the first day but does not rise on the second day. 0; The Dow Jones average does not rise on the first day but rises on the second day. 0; The Dow Jones average does not rise on either day. Let events A and B be the following: and each selects a car. The customers do not know each other, and there is no communication between them. Let the events A and B be defined as follows: A: The customers select at least one Toyota. B: The customers select two cars of the same model. A: The Dow Jones average rises on the first day. B: The Dow Jones average rises on the second day. a. Identify all pairs of cars in the sample space. b. Define event A. a. Show that (ANB) U (ĀNB) = B. b. Show that AU (ĀnB) = AUB. c. Define event B. d. Define the complement of A. e. Show that (AnB) U (ĀNB) = B. f. Show that A U (ANB) = AUB. 3.7 Florin Frenti operates a small, used car lot that has three Mercedes (M, M, M,) and two Toyotas (T, T,). Two customers, Cezara and Anda, come to his lot,
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