Use counting arguments from the preceding chapter. The seven contenders in a horse race at Aqueduct on a certain day, were Par None, Expect a Ship, All That Glitters, Senatorial Hope, Celera, Cliff Jumper, and Mayan Ring. You are interested in the first three places (winner, second place, and third place) for the race. (a) Find the cardinality n(S) of the sample space S of all possible finishes of the race. (A finish for the race consists of a first, a second, and a third place winner.) possible finishes (b) Let E be the event that Senatorial Hope is in second or third place, and let F be the event that Celera is the winner. Express the event En F in words. O This is the event that Celera wins and Senatorial Hope is in second place. O This is the event that Celera does not win and Senatorial Hope is in second or third place. O This is the event that Celera does not win and Senatorial Hope is not in second or third place. O This is the event that Celera wins and Senatorial Hope is in third place. O This is the event that Celera wins and Senatorial Hope is in second or third place. Find its cardinality. events Suppose two dice (one red, one green) are rolled. Consider the following events: A: the red die shows 1; B: the numbers add to 5; C: at least one of the numbers is 3; and D: the numbers do not add to 11. Express the given event in symbolic form. The red die shows 1, but the numbers do not add to 11. O AND' O A'U D O AND O AUD' A'ND How many elements does it contain?
Use counting arguments from the preceding chapter. The seven contenders in a horse race at Aqueduct on a certain day, were Par None, Expect a Ship, All That Glitters, Senatorial Hope, Celera, Cliff Jumper, and Mayan Ring. You are interested in the first three places (winner, second place, and third place) for the race. (a) Find the cardinality n(S) of the sample space S of all possible finishes of the race. (A finish for the race consists of a first, a second, and a third place winner.) possible finishes (b) Let E be the event that Senatorial Hope is in second or third place, and let F be the event that Celera is the winner. Express the event En F in words. O This is the event that Celera wins and Senatorial Hope is in second place. O This is the event that Celera does not win and Senatorial Hope is in second or third place. O This is the event that Celera does not win and Senatorial Hope is not in second or third place. O This is the event that Celera wins and Senatorial Hope is in third place. O This is the event that Celera wins and Senatorial Hope is in second or third place. Find its cardinality. events Suppose two dice (one red, one green) are rolled. Consider the following events: A: the red die shows 1; B: the numbers add to 5; C: at least one of the numbers is 3; and D: the numbers do not add to 11. Express the given event in symbolic form. The red die shows 1, but the numbers do not add to 11. O AND' O A'U D O AND O AUD' A'ND How many elements does it contain?
Chapter8: Sequences, Series,and Probability
Section8.6: Counting Principles
Problem 74E: Lottery Powerball is a lottery game that is operated by the Multi-State Lottery Association and is...
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Transcribed Image Text:Use counting arguments from the preceding chapter.
The seven contenders in a horse race at Aqueduct on a certain day, were Par None, Expect a Ship, All That Glitters, Senatorial Hope, Celera, Cliff Jumper, and Mayan Ring. You are interested in the first three
places (winner, second place, and third place) for the race.
(a) Find the cardinality n(S) of the sample space S of all possible finishes of the race. (A finish for the race consists of a first, a second, and a third place winner.)
possible finishes
(b) Let E be the event that Senatorial Hope is in second or third place, and let F be the event that Celera is the winner. Express the event En F in words.
O This is the event that Celera wins and Senatorial Hope is in second place.
O This is the event that Celera does not win and Senatorial Hope is in second or third place.
O This is the event that Celera does not win and Senatorial Hope is not in second or third place.
O This is the event that Celera wins and Senatorial Hope is in third place.
O This is the event that Celera wins and Senatorial Hope is in second or third place.
Find its cardinality.
events
Transcribed Image Text:Suppose two dice (one red, one green) are rolled. Consider the following events: A: the red die shows 1; B: the numbers add to 5; C: at least one of the numbers is 3; and D: the numbers do not add to 11. Express
the given event in symbolic form.
The red die shows 1, but the numbers do not add to 11.
O AND'
O A'U D
O AND
O AUD'
A'ND
How many elements does it contain?
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