1. Math 145 September 18, 2007

2. 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. 1. Tossing a coin: S1 = {H, T}. 2. Tossing a coin 3 times: S2 = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}. 3. Rolling a die: S3 = {1, 2, 3, 4, 5, 6} 4. 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

3. 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)

4. 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♥} = {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♣}

5. Rolling a Pair of Dice  Event – A subset of the sample space. 1. 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)}

6. 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)

7. 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)

8. 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)

9. 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

10. Thank you!