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Introduction Cards Combining Probabilities. Introduction. 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. 1 2. 1 2. P(Head) =. P(Tail) =. __. __.

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## Introduction Cards Combining Probabilities

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**Introduction**Cards Combining Probabilities**Introduction**• 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.**1**2 1 2 P(Head) = P(Tail) = __ __ Toss one coin, assume it is a fair coin and ignore the chance of it landing on its edge. There are only two possible outcomes – either a head H or a tail T. H T**Number of times this event occurs**––––––––––––––––––––––––––––– P(event) = Total possible number of outcomes Definition The probability of an event occurring is:** Cards **• Consider a deck of cards. There are four suits called hearts, diamonds, clubs and spades.** Cards **• 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!**1**4 __ number of clubs in deck total number of cards 13 52 ___ P(Clubs) = = Cards **number of 2s in deck**total number of cards 1 13 4 52 __ ___ = P(2) = Cards **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.**Throw 2**Throw 1 number the same total outcomes 1 6 6 36 __ ___ = Dice 36 P(both same) =**Throw 2**Throw 1 number the same total outcomes 1 36 1 36 __ ___ = Dice 36 P(two 4s) =**Throw 2**Throw 1 11 36 ___ Dice 36 P(at least one 6) =**Throw 2**Throw 1 25 36 ___ Dice 36 P(not getting a 6) =**Throw 2**Throw 1 1 12 3 36 __ ___ = Dice 36 P(a total of 10) =**3**8 ___ Three or more events H HHH P(2 heads and 1 tail) = T HHT H H HTH H T T HTT H H THH T T THT T H TTH T TTT

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