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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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