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ExpectedExpectedOutcomesOutcomes
Stage 6 - Year 12Stage 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) P(Heads) ==
12
Expectation Expectation ==
12
x x 550000
= = 225500
3
Example: Example: How many head/heads can be expected when two coins are tossed 200 times
HH TT
HH
TT
HH HH HH TT
TT HH TT TT
P(Head/Head) P(Head/Head) ==
1
Expectation Expectation ==
14
x x 220000
= 50= 50
4
4
Example: Example: How many tails/tails can be expected when two coins are tossed 200 times
HH TT
HH
TT
HH HH HH TT
TT HH TT TT
P(Tails/Tails) P(Tails/Tails) ==
1
Expectation Expectation ==
14
x x 220000
= 50= 50
4
5
Example: Example: How many heads/tails can be expected when two coins are tossed 200 times
HH TT
HH
TT
HH HH HH TT
TT HH TT TT
P(Head/Tails) P(Head/Tails) ==
2
Expectation Expectation ==
12
x x 220000
= = 110000
412==
6
HH
1122334455667788991010111112121313141415151616171718181919202021212222232324242525
TT
1122334455667788991010111112121313141415151616171718181919202021212222232324242525
Tossing a Coin ExperimentTossing a Coin Experiment
Click HereClick 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
5252 1212P(Picture Card) P(Picture Card)
==
1122
5522
== 3311
33Expected Expected ==
3311
33
x 26x 26 = 6= 6
8
Expected Outcomes
Expected number of Expected number of Picture CardsPicture Cards is is 66 out of out of 2626..
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9
Reset
Slot Machine
Arrangements = 3x 3 x 3= 27
You win if you have two or more of the same type of
fruit.All fruit different = 3x 2 x 1= 6
P( All fruit different) = 627
29
=
P( Two or more same) = 1 29
- 79
=
Expectation of winning in 9 games?
Expectation = 9 79
x = 7 wins.
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