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What is probability?

What is probability?. The Weather Forecast Winning the Super 5 or a Lottery Arriving first in a race. Certain Sunday comes after Saturday We need to eat and drink every day . Impossible I win the lottery without buying a ticket The sun will not rise tomorrow. Certain or Impossible?.

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What is probability?

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  1. What is probability? • The Weather Forecast • Winning the Super 5 or a Lottery • Arriving first in a race

  2. Certain Sunday comes after Saturday We need to eat and drink every day Impossible I win the lottery without buying a ticket The sun will not rise tomorrow Certain or Impossible? 1) Sunday comes after Saturday 3) The sun will not rise tomorrow 2) I win the lottery without buying a ticket 4) We need to eat and drink every day

  3. Likely or Unlikely? • Mary never does her homework and does not study? Will she pass the exam? • John takes good care of a plant, he waters it, gives it fertilizer etc.. Will the plant grow and not die?

  4. Evens This is why coin flipping has been used as a means of solving disputes for centuries! Coin flipping is a method that trusts the decision to pure luck, It is generally assumed that the outcome is unpredictable, with equal probabilities for the two outcomes. Today we often see people flip a coin at the beginning of several sports matches, such as football. An equal chance of something happening or not happening is called EVENS

  5. Probability of an event Mary passes exam if she never does her homework or studies If I take good care of a plant by watering it, giving it fertilizer etc.. It will grow and not die unlikely likely evens Impossible Certain Tossing a coin and getting a head I live without eating or drinking Sunday comes after Saturday

  6. link to view a virtual Spinner Spinners

  7. Spinners

  8. Chances of Spinning Blue Impossible Certain Impossible Very Unlikely Equally likely Very likely Certain = 1 = 0 =

  9. Die • Dice have been used throughout Asia since before recorded history. • The oldest know dice were excavated at the Burnt City archaeological site in south-eastern Iran. • In China, India, Japan, Korea and other Asiatic countries, dice have always been popular and are still. The marking on Chinese dominoes evolved from the markings on dice, taken two at a time.

  10. How can I never get a 1 or a 6!! How difficult is it to get a 1 or 6 when tossing a die?

  11. Tossing a die P(1) = P(2) = P(3) = P(4) = P(5) = P(6) = P (getting a 1) = P (getting a 2) = P (getting a 6) =

  12. Probability an event does NOT occur P(not 1) = P(getting a 2,3,4,5 or 6) = P(getting a 1) = P(getting one from all possibilities) = P(getting a 1,2,3,4,5 or 6) = P(not 1) = P(all possibilities) – P(1) = - = So P(event does not occur) = 1 – P(event occurs)

  13. Beads in a bag P(picking a red bead) = P(picking a red bead) = P(picking a black bead) = P(picking a black bead) =

  14. Using a pack of cards If a card is drawn at random from a pack of 52, find the probability that it is: • a king • a heart P(king) = = P(heart) = =

  15. Students’ School transport 70% of the Maltese students go to school by bus. The other students are driven to school by their parents. What is the probability that a student chosen at random has been driven to school by his parents? 70% use bus = 70 out of 100 students => 30 out of 100 students go to school driven by parents P(student uses family transport) = =

  16. On a bus there are 48 passengers. 20 are men and 28 are women. A passenger is chosen at random. What is the probability that the passenger is: female male Passengers on a bus P(female) = = P(male) = =

  17. A bag contains 4 pink beads, 3 blue beads and 3 green beads. If 1 bead is drawn at random from the bag, find the probability that the bead is: Pink not blue yellow Colourful beads in a bag P(pink) = = P(not blue) = 1 – P(blue) = 1 - = P(yellow) = = 0

  18. Possibility Spaces You own a skirt, a jeans and a pair of trousers. You also have a pink top, a blue top and a white top. How many different combinations can you create so that you will not look the same everyday? On one day I can wear the • skirt + pink top • Skirt + blue top • Skirt + white top • Jeans + pink top • Jeans + blue top • Jeans + white top • Trouser + pink top • Trousers + blue top • Trousers + white top

  19. The Fruit Machine The fruit machine has 2 windows. Each window can show a water melon, cherries, strawberries and pineapples. To win the game the set of fruit appearing in the 2 windows should be the same. What is the probability of getting a water melon and a pineapple? What is the probability of winning the game? What is the probability of not winning?

  20. P(water melon and pineapple) = = P(winning the game) = = P(not winning) = = OR P(not winning) = 1 – P(winning) = 1 - =

  21. Tossing two dice at the same time • A game is played using two dice. The player can play again if the number on the two dice is the same. • Draw a possibility space illustrating all the possible combinations when throwing two dice. • What is the probability the player obtains a 6 in at least one of the dice? • What is the probability the player can play again

  22. P(getting at least one 6) = P(player plays again) = =

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