Math 145

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Math 145

• February 1, 2006

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Terminologies in Probability

• Experiment Any process that produces an outcome
  that cannot be predicted with certainty.
• Example tossing a coin, rolling dice, picking a
  card, doing a survey, conducting experimental
  studies.
• Sample Space Set of all possible outcomes.
• Tossing a coin S1 H, T.
• Tossing a coin 3 times
• S2 HHH, HHT, HTH, THH, HTT, THT, TTH, TTT.
• Rolling a die S3 1, 2, 3, 4, 5, 6
• Picking a card from the standard deck of cards
• S4 A?, 2?,, 10?, J?, Q?, K?, A?, , K?,
• A?,, K?, A?, , K?. Total of 52 cards

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Rolling a Pair of Dice

• S5

(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)
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Terminologies in Probability

• Event A subset of the sample space.
• Picking a card from the standard deck of cards
• S4 A?, 2?,, 10?, J?, Q?, K?, A?, , K?,
• A?,, K?, A?, , K?. Total of 52 cards
• E1 The event of selecting a heart.
• A?, 2?,, 10?, J?, Q?, K?
• E2 The event of selecting a face card.
• J?, Q?, K?, J?, Q?, K?, J?, Q?, K?, J?, Q?,
  K?

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Rolling a Pair of Dice

• Event A subset of the sample space.
• Rolling a pair of dice.
• E3 The event of getting doubles.
• (1,1), (2,2), (3,3), (4,4), (5,5), (6,6)
• E4 The event of getting a sum of 6.
• (1,5),(5,1),(2,4),(4,2),(3,3)
• E5 The event of getting at least one 5.
• (1,5),(2,5),(3,5),(4,5),(5,5),(6,5),(5,6),
  (5,4),(5,3),(5,2),(5,1)

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Rolling a Pair of Dice

• E3

(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)
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Rolling a Pair of Dice

• E4

(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)
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Rolling a Pair of Dice

• E5

(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)
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Terminologies in Probability

• Experiment Any process that generates data.
• Sample Space Set of all possible outcomes.
• Event A subset of the sample space.
• Probability (of an event) The chance of this
  event occurring.
• P(E) no. of favorable / no. of possible

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Thank you!