Quit Introduction Cards Combining Probabilities Quit Introduction Probability
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Introduction Cards Combining Probabilities Quit
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. Quit
• 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 P(Head) = Quit T 1 __ 2 P(Tail) = 1 __ 2
Definition The probability of an event occurring is: Number of times this event occurs P (event) = ––––––––––––––– Total possible number of outcomes Quit
Cards • Consider a deck of cards. There are four suits called hearts, diamonds, clubs and spades. Quit
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! Quit
Cards Clubs A 2 3 4 5 6 7 8 9 10 J Q K Diamonds A 2 3 4 5 6 7 8 9 10 J Q K Hearts A 2 3 4 5 6 7 8 9 10 J Q K Spades A 2 3 4 5 6 7 8 9 10 J Q K P(Clubs) = Quit 13 ___ 52 number of clubs in deck 1 __ = total number of cards 4
Cards Clubs A 2 3 4 5 6 7 8 9 10 J Q K Diamonds A 2 3 4 5 6 7 8 9 10 J Q K Hearts A 2 3 4 5 6 7 8 9 10 J Q K Spades A 2 3 4 5 6 7 8 9 10 J Q K P(2) = Quit 4 ___ 52 number of 2 s in deck total number of cards = 1 __ 13
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. Quit
Dice Throw 1 Quit 1 2 3 4 5 6 1 1, 2 1, 3 1, 4 1, 5 1, 6 2 2, 1 2, 2 2, 3 2, 4 2, 5 2, 6 3 3, 1 3, 2 3, 3 3, 4 3, 5 3, 6 4 4, 1 4, 2 4, 3 4, 4 4, 5 4, 6 5 5, 1 5, 2 5, 3 5, 4 5, 5 5, 6 6 6, 1 6, 2 6, 3 6, 4 6, 5 6, 6 P(both same) = 6 ___ 36 number the same total outcomes Throw 2 36 = 1 __ 6
Dice Throw 1 Quit 1 2 3 4 5 6 1 1, 2 1, 3 1, 4 1, 5 1, 6 2 2, 1 2, 2 2, 3 2, 4 2, 5 2, 6 3 3, 1 3, 2 3, 3 3, 4 3, 5 3, 6 4 4, 1 4, 2 4, 3 4, 4 4, 5 4, 6 5 5, 1 5, 2 5, 3 5, 4 5, 5 5, 6 6 6, 1 6, 2 6, 3 6, 4 6, 5 6, 6 P(two 4 s) = 1 ___ 36 Throw 2 36 number the same __ 1 = total outcomes 36
Dice Throw 1 Quit 1 2 3 4 5 6 1 1, 2 1, 3 1, 4 1, 5 1, 6 2 2, 1 2, 2 2, 3 2, 4 2, 5 2, 6 3 3, 1 3, 2 3, 3 3, 4 3, 5 3, 6 4 4, 1 4, 2 4, 3 4, 4 4, 5 4, 6 5 5, 1 5, 2 5, 3 5, 4 5, 5 5, 6 6 6, 1 6, 2 6, 3 6, 4 6, 5 6, 6 P(at least one 6) = 11 ___ 36 Throw 2 36
Dice Throw 1 Quit 1 2 3 4 5 6 1 1, 2 1, 3 1, 4 1, 5 1, 6 2 2, 1 2, 2 2, 3 2, 4 2, 5 2, 6 3 3, 1 3, 2 3, 3 3, 4 3, 5 3, 6 4 4, 1 4, 2 4, 3 4, 4 4, 5 4, 6 5 5, 1 5, 2 5, 3 5, 4 5, 5 5, 6 6 6, 1 6, 2 6, 3 6, 4 6, 5 6, 6 P(not getting a 6) = 25 ___ 36 Throw 2 36
Dice Throw 1 Quit 1 2 3 4 5 6 1 1, 2 1, 3 1, 4 1, 5 1, 6 2 2, 1 2, 2 2, 3 2, 4 2, 5 2, 6 3 3, 1 3, 2 3, 3 3, 4 3, 5 3, 6 4 4, 1 4, 2 4, 3 4, 4 4, 5 4, 6 5 5, 1 5, 2 5, 3 5, 4 5, 5 5, 6 6 6, 1 6, 2 6, 3 6, 4 6, 5 6, 6 3 ___ 1 __ P(a total of 10) = 36 = 12 Throw 2 36
Three or more events P(2 heads and 1 tail) = H T Quit 3 ___ 8 H HHH T HHT H HTH T T HTT H H THH T THT H TTH T TTT H T
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