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Quit

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Introduction Cards Combining Probabilities

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QuitIntroduction Probability is the maths of chance and gambling, telling us how likely an event is to occur. The probability of an event occurring is usually written as a fraction or as a percentage.

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Quit Toss one coin, assume it is a fair coin and ignore the chance of it landing on its edge. P(Head) = 1212 __ TH There are only two possible outcomes – either a head H or a tail T. P(Tail) = 1212 __

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QuitDefinition The probability of an event occurring is: P (event) = Total possible number of outcomes Number of times this event occurs –––––––––––––––––––––––––––––

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Quit Consider a deck of cards. There are four suits called hearts, diamonds, clubs and spades. Cards Cards

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Quit Consider a deck of cards. There are four suits called hearts, diamonds, clubs and spades. In each of these there are 13 cards – an ace, the numbers 2 to 10 inclusive, and the picture cards: jack, queen and king. This makes a total of 52 cards in an ordinary deck. Some games require one extra card, the Joker. We will not use this extra card. If the cards are boxed (shuffled or mixed) and then 13 cards dealt to each of four people, the chances of a particular person getting 13 clubs are 635,013,559,600 to 1. This is more than the number of seconds in 20,000 years! Cards Cards

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Quit Clubs A2345678910JQK Diamonds A2345678910JQK Hearts A2345678910JQK Spades A2345678910JQK P(Clubs) = 13 52 ___ Cards Cards number of clubs in deck total number of cards = 1414 __

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Quit Clubs A2345678910JQK Diamonds A2345678910JQK Hearts A2345678910JQK Spades A2345678910JQK P(2) = 4 52 ___ Cards Cards number of 2s in deck total number of cards = 1 13 __

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Quit Combining Probabilities If two events happen simultaneously, a sample space can be constructed to see clearly the possible outcomes. A sample space involves putting all the possible outcomes of one event on one axis of a grid and all the possible outcomes of a second event on the other axis.

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Quit 123456 11, 11, 21, 31, 41, 51, 6 22, 12, 22, 32, 42, 52, 6 33, 13, 23, 33, 43, 53, 6 44, 14, 24, 34, 44, 54, 6 55, 15, 25, 35, 45, 55, 6 66, 16, 26, 36, 46, 56, 6 Dice Throw 2 Throw 1 36 P(both same) = 6 36 ___ number the same total outcomes = 1 6 __

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Quit 123456 11, 11, 21, 31, 41, 51, 6 22, 12, 22, 32, 42, 52, 6 33, 13, 23, 33, 43, 53, 6 44, 14, 24, 34, 44, 54, 6 55, 15, 25, 35, 45, 55, 6 66, 16, 26, 36, 46, 56, 6 Dice Throw 2 Throw 1 36 P(two 4s) = 1 36 ___ number the same total outcomes = 1 36 __

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Quit 123456 11, 11, 21, 31, 41, 51, 6 22, 12, 22, 32, 42, 52, 6 33, 13, 23, 33, 43, 53, 6 44, 14, 24, 34, 44, 54, 6 55, 15, 25, 35, 45, 55, 6 66, 16, 26, 36, 46, 56, 6 Dice Throw 2 Throw 1 36 P(at least one 6) = 11 36 ___

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Quit 123456 11, 11, 21, 31, 41, 51, 6 22, 12, 22, 32, 42, 52, 6 33, 13, 23, 33, 43, 53, 6 44, 14, 24, 34, 44, 54, 6 55, 15, 25, 35, 45, 55, 6 66, 16, 26, 36, 46, 56, 6 Dice Throw 2 Throw 1 36 P(not getting a 6) = 25 36 ___

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Quit 123456 11, 11, 21, 31, 41, 51, 6 22, 12, 22, 32, 42, 52, 6 33, 13, 23, 33, 43, 53, 6 44, 14, 24, 34, 44, 54, 6 55, 15, 25, 35, 45, 55, 6 66, 16, 26, 36, 46, 56, 6 Dice Throw 2 Throw 1 36 P(a total of 10) = 3 36 ___ = 1 12 __

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Quit Three or more events T H T H T H T H H T H T T H HHH HHT HTH HTT THH THT TTH TTT P(2 heads and 1 tail) = 3 8 ___

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