JIM SMITH JCHSJIM SMITH JCHS

SPI 3108.5.1

THE PROBABILITY THAT THE PROBABILITY THAT SOMETHING WILL HAPPEN IS SOMETHING WILL HAPPEN IS

THE NUMBER OF SUCCESSFULTHE NUMBER OF SUCCESSFULOUTCOMES OVER THE TOTAL OUTCOMES OVER THE TOTAL

NUMBER OF OUTCOMES.NUMBER OF OUTCOMES.

LET’S LOOK AT A DIE. IF YOU ROLL ONE LET’S LOOK AT A DIE. IF YOU ROLL ONE

DIE, THERE IS ONLY DIE, THERE IS ONLY 11 WAY TO WAY TO

GET A GET A 33 SO SO 11 WILL BE THE WILL BE THE

NUMBER OF SUCCESSFUL OUTCOMES. NUMBER OF SUCCESSFUL OUTCOMES.

YOU CAN ROLL ANY ONE OF YOU CAN ROLL ANY ONE OF 66

NUMBERS SO THERE ARE NUMBERS SO THERE ARE 66 POSSIBLE POSSIBLE

OUTCOMES. OUTCOMES. 66 WILL BE THE TOTAL NUMBER WILL BE THE TOTAL NUMBER

OF OUTCOMES. WITH OF OUTCOMES. WITH 11 DIE THE DIE THE

PROBABILITY OF ROLLING A PROBABILITY OF ROLLING A 33 IS IS

11//66

WHAT IS THE PROBABILITY OF WHAT IS THE PROBABILITY OF ROLLING A 5?ROLLING A 5?

WHAT IS THE PROBABILITY OFWHAT IS THE PROBABILITY OF ROLLING A 2?ROLLING A 2?

WHAT IS THE PROBABILITY OFWHAT IS THE PROBABILITY OF ROLLING A 7?ROLLING A 7?

LET’S USE 2 DICE. NOW OUR LET’S USE 2 DICE. NOW OUR NUMBERS CHANGE. THE TOTAL NUMBERS CHANGE. THE TOTAL

NUMBER OF POSSIBLE OUTCOMESNUMBER OF POSSIBLE OUTCOMESINCREASES. FOR EVERY NUMBER INCREASES. FOR EVERY NUMBER

WE CAN ROLL ON ONE DIE, WE CAN ROLL ON ONE DIE, WE CAN ROLL ONE OF SIX NUMBERS WE CAN ROLL ONE OF SIX NUMBERS

ON THE SECOND DIE.ON THE SECOND DIE.

HERE IS A TABLEHERE IS A TABLEDIE 1 DIE 2DIE 1 DIE 2

11 1,2,3,4,5,61,2,3,4,5,622 1,2,3,4,5,61,2,3,4,5,633 1,2,3,4,5,61,2,3,4,5,644 1,2,3,4,5,61,2,3,4,5,655 1,2,3,4,5,61,2,3,4,5,666 1,2,3,4,5,6 1,2,3,4,5,6

36 possibilities36 possibilities

HOW MANY WAYS CAN YOU HOW MANY WAYS CAN YOU ROLL A 5?ROLL A 5?

Die 1 Die 2Die 1 Die 222 4433 3344 2255 11

4 SUCCESSFUL OUTCOMES4 SUCCESSFUL OUTCOMES

WHAT IS THE PROBABILITY OFWHAT IS THE PROBABILITY OFROLLING A 5 WITH 2 DICE?ROLLING A 5 WITH 2 DICE?

4/36 or 1/94/36 or 1/9

PROBABILITY THAT INVOLVESPROBABILITY THAT INVOLVESA GEOMETRIC MEASUREMENTA GEOMETRIC MEASUREMENT

SUCH AS LENGTH ORSUCH AS LENGTH OR AREA IS CALLED AREA IS CALLED

LET’S LOOK AT GAME BOARDSLET’S LOOK AT GAME BOARDS

THE PROBABILITY THE PROBABILITY THAT A DART WILL THAT A DART WILL

HIT A CERTAIN HIT A CERTAIN COLOR IS…. COLOR IS….

THE AREA OF THAT THE AREA OF THAT COLOR OVER THE COLOR OVER THE

AREA OF THE AREA OF THE WHOLE BOARD.WHOLE BOARD.

IF THE BOARD IS DIVIDED INTO 4 EQUALIF THE BOARD IS DIVIDED INTO 4 EQUALPARTS THEN….PARTS THEN….

THE PROBABILITY OFTHE PROBABILITY OF HITTING GREEN ISHITTING GREEN IS

1/41/4THE PROBABILITY OFTHE PROBABILITY OF HITTING BLUE ISHITTING BLUE IS

2/4 = 1/22/4 = 1/2THE PROBABILITY OFTHE PROBABILITY OF HITTING BLACK ISHITTING BLACK IS

1/41/4

FIND FIND THE PROBABILITY OF THE PROBABILITY OF A DART LANDING INA DART LANDING IN

THE DARK BLUETHE DARK BLUE

10/25 = 2/510/25 = 2/5

THE LIGHT BLUETHE LIGHT BLUE 7/257/25

THE BROWNTHE BROWN 3/253/25

THE GREENTHE GREEN 5/25 = 1/55/25 = 1/5

66

66

FIND FIND THE PROBABILITY OF THE PROBABILITY OF A DART LANDING INA DART LANDING INTHE BLACK AREATHE BLACK AREA

66

66

AREA OF SQUARE – AREA OF CIRCLEAREA OF SQUARE – AREA OF CIRCLE OVEROVER AREA OF SQUAREAREA OF SQUARE

66

66

AREA OF SQUARE – AREA OF CIRCLEAREA OF SQUARE – AREA OF CIRCLE OVEROVER AREA OF SQUAREAREA OF SQUARE

36 - 936 - 9ππ 3636

(6X6) – ((6X6) – (ππ3²)3²) (6X6)(6X6)

33

44

44

11== 4 – 4 – ππ

44

6060°°

FIND THE PROBABILITYFIND THE PROBABILITYOF A SPINNER STOPINGOF A SPINNER STOPING

ON….ON….

GREENGREEN 90/360 = 1/490/360 = 1/4.25 = 25%.25 = 25%

BLUEBLUE 60/360 = 1/660/360 = 1/6.17 = 17%.17 = 17%

YELLOWYELLOW 250/360 = 25/36250/360 = 25/36.694 = 69%.694 = 69%