All examples sourced from: Mathematical Studies SL, by Mal Coad et al., Haese & Harris Publications, 2nd Ed 2010

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  The sample space of an event is a listing / picture or diagram of all the possible outcomes for that event (or experiment).

  The most common diagrams used to construct the sample space are: ›  Simply writing the outcomes in a list ›  Using a two-by-two table ›  Drawing a tree diagram ›  Drawing a venn diagram

  Where it is often referred to as the universal set U

  (i) List the sample space for (a) tossing a coin (b) rolling a die

  (ii) Use a tree diagram to write the sample space when: (a) tossing two coins (b) drawing 3 marbles from a

bag with red and yellow marbles

  Theoretical Probability is, sometimes called classical probability, is defined as:

›  Remember this is different to Experimental Probability because that is based on a particular experiment or trial and the relative frequency calculated by that trial.

›  The difference can almost be described as theoretical being the “expected” probability and experimental as the “actual” probability.

›  In reality the experimental approaches the theoretical over time with many many trials.

  Hence the P(coin will land heads up) = ½ or P(choosing a diamond from a deck of cards) = ¼

  Repeating an experiment one time or a hundred times has no effect on the “theoretical probability”, it remains the same.

P(event occuring) = number of times event occurstotal number of possible outcomes

P A( ) = n A( )n U( )

  The complementary probability of an event is the “NOT” case

›  e.g if there is a 35% chance of rain tomorrow, there must be a 65% chance that it will not rain.

Example 3   Find the probability that when rolling two dice they do not

show doubles. ›  Rolling two die gives a total of 6 x 6 = 36 possible outcomes ›  Doubles are 1,1 and 2,2, … to 6,6 hence there are 6 outcomes. ›  P(not doubles) = 1 – P(doubles) = 1 – 6/36 = 30/36 = 5/6

P(event not occuring) = P A '( )P A '( ) = 1− P A( )