1 Press Ctrl-A ©G Dear2010 – Not to be sold/Free to use ExpectedOutcomes Stage 6 - Year 12 General Mathematic (HSC)

2 Expected Outcomes Is the number of times an event can be expected to occur in a given number of trials. The number of times an event occurs (experimental) is not the same as theoretical. Example: Example: How many heads can be expected when a coin is tossed 500 times P(Heads) = 1212 Expectation = 1212 x 500 = 250

3 Example: Example: How many head/heads can be expected when two coins are tossed 200 times HT H T H HH HH HH H H TH TH TH T T HT HT HT H T TT TT TT T P(Head/Head) = 1 Expectation = 1414 x 200 = 50 4

4 Example: Example: How many tails/tails can be expected when two coins are tossed 200 times HT H T H HH HH HH H H TH TH TH T T HT HT HT H T TT TT TT T P(Tails/Tails) = 1 Expectation = 1414 x 200 = 50 4

5 Example: Example: How many heads/tails can be expected when two coins are tossed 200 times HT H T H HH HH HH H H TH TH TH T T HT HT HT H T TT TT TT T P(Head/Tails) = 2 Expectation = 1212 x 200 = =

6 H T Do Not Delete Tossing a Coin Experiment Click Here

7 Expected Outcomes Example: Example: How many ‘picture cards’ can be expected when 26 cards are chosen from a standard deck of playing cards P(Picture Card) = 1252 = 313 Expected = 313 x 26 = 6

8 Expected Outcomes Expected number of Picture Cards is 6 out of 26. Free on the web:

9 Reset Slot Machine Arrangements = 3x 3 = 27 You win if you have two or more of the same type of fruit. All fruit different = 3 x 2x 1= 6 P( All fruit different) = = P( Two or more same) = = Expectation of winning in 9 games? Expectation = x = 7 wins Win Lose Reset Scores