AM40SFeb19

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AM40SFeb19

  1. 1. * Experimental and Theoretical Probability In a family of three children, what is the probability that 2 of the children will be girls? Blaise Pascal Pierre de Fermat The Story of Probability The Chevalier de Mere, a rich Frenchman who liked gambling, was responsible for inviting the philosopher and mathematician Blaise Pascal to carry out some of the earliest work on probability theory. De Mere played a gambling game in which he bet that he could throw a six in four throws of a die. De Mere progressed from this game to betting that with two dice he could throw a double six in 24 throws. It was known that the odds were in his favour with the first game, and gamblers of the time reckoned that as four is to six (the numbers of ways a die can fall) as 24 is to 36 (the ways two dice can fall), the second game should be favourable. The Chevalier de Mere was not satisfied with this assumption and asked Pascal to work out the true probabilities. Source: http://www.probabilitytheory.info/topics/periodic_events.htm Photo source: http://flickr.com/photos/phitar/7971517/
  2. 2. Terms you should know ... PROBABILITY: The branch of mathematics that deals with chance SAMPLE SPACE: The set of all possible things that can happen for a given set of circumstances Example: rolling a die-6, the sample space would be {1, 2, 3,4,5, 6} because these are all the possible outcomes. EVENT (E): An event is a subset of the sample space. It is one particular outcome for a given set of circumstances. SIMPLE EVENTS: The result of an experimental carried out in 1 step. Example: Flip a coin. The result is Heads. COMPOUND EVENT: The result of an experimental carried out in more than one step. Example: Flip a coin and roll a die. The result is heads and 6. Calculating the Probability of an Event Probability Can Be Expressed As: • a ratio • a fraction • a decimal • a percent CERTAIN EVENTS: An events whose probability is equal to 1. IMPOSIBLE EVENTS: An event whose probability is equal to 0. IMPORTANT: Probability is always a number between 0 and 1.
  3. 3. Write your answers as fractions reduced to lowest terms. 1. What is the probability that a woman will win the Oscar Award for Best Actress? 2. What is the probability that a 7 shows when rolling a normal six-sided die? 3. What is the probability that a king is drawn from a normal deck of 52 cards?
  4. 4. 4. A bag contains eight blue and five white marbles. What is the probability of randomly selecting a white marble? 5. A bag contains five red, four green, and three black candies. What is the probability that you do not select a black candy if you randomly select one?
  5. 5. Complementary Events The complement of an event, E, is writtin as either E' or E. The complement of an event refers to the case where E does not occur. Example: H = Drawing a heart from a deck of cards. H'(the complement) = Drawing a card that is not a heart. Calculating complementary probabilities ... P(E) + P(E') = 1 so ... P(E) = 1 – P(E') or P(E') = 1 – P(E) Understanding the concept ... If there are 52 players in a sudden death singles tennis tournament, how many games must be played in order to determine the winner?
  6. 6. In a family of three children, what is the probability that 2 of the children will be girls? Experimental Probability: The chances of something happening, based on repeated testing and observing results. It is the ratio of the number of times an event occurred to the number of times tested. For example, to find the experimental probability of winning a game, one must play the game many times, then divide the number of games won by the total number of games played.

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