2. 1 Press Ctrl-A ©G Dear2010 – Not to be sold/Free to use ExpectedOutcomes Stage 6 - Year 12 General Mathematic (HSC)

3. 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

4. 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

5. 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

6. 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 = 100 4 1 2 =

7. 6 H 12345678910111213141516171819202122232425 T 12345678910111213141516171819202122232425 Do Not Delete Tossing a Coin Experiment Click Here

8. 7 Expected Outcomes Example: Example: How many ‘picture cards’ can be expected when 26 cards are chosen from a standard deck of playing cards 52 12 P(Picture Card) = 1252 = 313 Expected = 313 x 26 = 6

9. 8 Expected Outcomes Expected number of Picture Cards is 6 out of 26. Free on the web: www.crickweb.co.uk/assets/resources/flash.php?&file=CardFlip1

10. 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) = 6 27 2929 = P( Two or more same) = 1 2929 - 7979 = Expectation of winning in 9 games? Expectation = 9 7979 x = 7 wins. 123456789 Win 123456789 Lose Reset Scores