Independent Events. Examples of independent events 1.You flip a coin and get a heads and you flip a second coin and get a tails. The two coins don't influence.

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Presentation transcript:

Independent Events

Examples of independent events 1.You flip a coin and get a heads and you flip a second coin and get a tails. The two coins don't influence each other. 2.The probability of rain today and the probability of a pop quiz. Quizzes happen, rain or shine. 3.The probability of a having a car crash in the next Km’s is independent of the number of car crashes you’ve had in the last Km’s.

Examples of non independent events 1.You draw one card from a deck and its black and you draw a second card and its black. By removing one black card, you made the probability of drawing a second one slightly smaller. Technically this is called 'sampling without replacement'. 2.The probability of snow today and the probability of a pop quiz; Snow causes school closings, in which case your teacher can't give you a pop quiz. 3.The chance that you are hungry right now and the chance that you're eating right now. One leads to the other eventually...

Mutually Exclusive Events Unable to both happen at the same time

Mutually Exclusive Example Consider rolling a dice. What is the probability or rolling a 2 or a 5? We can say rolling both is mutually exclusive. Or the probability of rolling a two and a five is zero. The probability of rolling a two or a five is 2/6 (1/6 + 1/6).

Mutually Exclusive Examples Two dice are rolled. We define events E1, E2, E3 and E4 as follows E1: Getting a sum equal to 10 E2: Getting a double E3: Getting a sum less than 4 E4: Getting a sum less than 7 a) Are events E1 and E2 mutually exclusive? b) Are events E2 and E3 mutually exclusive? c) Are events E3 and E4 mutually exclusive? d) Are events E4 and E1 mutually exclusive?

Mutually Exclusive Examples a) E1 and E2 are not mutually exclusive because outcome (5,5) is a double and also gives a sum of 10. The two events may occur at the same time. b) E2 and E3 are not mutually exclusive because outcome (1,1) is a double and gives a sum of 2 and is less than 4. The two events E2 and E3 may occur at the same time. c) E3 and E4 are not mutually exclusive a sum can be less than 7 and less than 4 a the same time. Example outcome (1,2). d) E4 and E1 are mutually exclusive because a sum less than 7 cannot be equal to 10 at the same time. The two events cannot occur at the same time.

Mutually Exclusive Events Unable to both happen at the same time

Complementary Events

Complementary Examples Consider a person being selected at random from a class of 30. The probability a male is selected is complementary to the probability a female is selected. If there were 20 males and 10 females then the probabilities would be 2/3 and 1/3 respectively. The probability of complementary events always add to 1!

Complementary examples 1.Consider the probability of rain…..The probability of no rain is complementary to the probability of rain. 2.The probability of the Black Caps winning the CWC is complementary with the probability of not winning the CWC.

Match the word with the definition WordDefinitions Sample SpaceOne ‘run through’ of an experiment TrialThe set of all possible outcomes Long run relative frequencyThe result of a single ‘run through’ OutcomeA good estimate of the true probability Theoretical ProbabilityThe calculation of probability from carrying out an experiment – often called experimental probability

Probability Notation Let A = The event NZ wins the CWC semi final Let B = The event SA wins the CWC semi final P(A) = P(A’) = P(A n B) = P(A u B) =