Terminologies in Probability Experiment Any process that produces

Terminologies in Probability Ø Ø Experiment – Any process that produces an outcome that cannot be predicted with certainty. Ø Example: tossing a coin, rolling dice, picking a card, doing a survey, conducting experimental studies. Sample Space – Set of all possible outcomes. 1. Tossing a coin: S 1 = {H, T}. 2. Tossing a coin 3 times: S 2 = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}. 3. Rolling a die: S 3 = {1, 2, 3, 4, 5, 6} 4. Picking a card from the standard deck of cards: S 4 = {A♥, 2♥, …, 10♥, J♥, Q♥, K♥, A♦, …, K♦, A♠, …, K♠, A♣, …, K♣}. Total of 52 cards

Rolling a Pair of Dice S 5 (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)

Terminologies in Probability Ø Event – A subset of the sample space. 1. Picking a card from the standard deck of cards: S 4 = {A♥, 2♥, …, 10♥, J♥, Q♥, K♥, A♦, …, K♦, A♠, …, K♠, A♣, …, K♣}. Total of 52 cards E 1 = The event of selecting a heart. = {A♥, 2♥, …, 10♥, J♥, Q♥, K♥} E 2 = The event of selecting a face card. = {J♥, Q♥, K♥, J♦, Q♦, K♦, J♠, Q♠, K♠, J♣, Q♣, K♣}

Rolling a Pair of Dice Ø Event – A subset of the sample space. 2. Rolling a pair of dice. E 3 = The event of getting doubles. ={(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)} E 4 = The event of getting a sum of 6. ={(1, 5), (5, 1), (2, 4), (4, 2), (3, 3)} E 5 = 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)}

Rolling a Pair of Dice E 3 (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)

Rolling a Pair of Dice E 4 (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)

Rolling a Pair of Dice E 5 (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)

Terminologies in Probability Ø Ø 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. Ø P(E) = sum of all the sample point probabilities in the event.