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Terminologies in Probability

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.

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Terminologies in Probability

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  1. 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

  2. Rolling a Pair of Dice S5

  3. Terminologies in Probability • Event – A subset of the sample space. 1. 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♣}

  4. Rolling a Pair of Dice • Event – A subset of the sample space. 2. 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)}

  5. Rolling a Pair of Dice E3

  6. Rolling a Pair of Dice E4

  7. Rolling a Pair of Dice E5

  8. 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) = sum of all the sample point probabilities in the event.

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