Probabilities that add to 1

The Maths Habit

A spinner lands on red, blue or green. The whole bar is everything that can happen. Which bar can be right?

RedBlueGreen
A✓ Fills the barBA gap is leftCToo much

The bar has 10 parts. How many parts are not shaded?

3 + ? = 107
6 + ? = 104
9 + ? = 101

Outcome
One possible result.
Red
Probability
How likely an outcome is. It is a number from 0 to 1.
01impossiblecertain
Certain
Sure to happen. Its probability is 1.
whole = 1

whole = 1what you knowleft
1−what you know=left
  1. 1Shade what you know.The whole bar is 1. Each part is 0.1.
  2. 2Take it away from 1.What is left is the answer.

The probability it rains tomorrow is 0.3. Work out the probability it does not rain.

1Shade what you know.
whole = 10.30.7
2Take it away from 1.
1−0.3=0.7

The probability a bus is late is 0.2. Work out the probability it is not late.

1Shade what you know.
whole = 10.2?0.8
2Take it away from 1.
1−0.2=0.8

The probability it rains tomorrow is 0.3. Work out the probability it does not rain.

1Shade what you know.
whole = 10.30.7
2Take it away from 1.
1−0.3=0.7
1what you knowleft21−what you know=left

The probability a spinner lands on red is 0.6. Work out the probability it does not land on red.

1Shade what you know.
whole = 10.6?0.4
2Take it away from 1.
1−0.6=0.4

The probability it rains tomorrow is 0.3. Work out the probability it does not rain.

1Shade what you know.
whole = 10.30.7
2Take it away from 1.
1−0.3=0.7
1what you knowleft21−what you know=left

The probability a train is late is 0.4. Work out the probability it is not late.

1Shade what you know.
whole = 10.4?0.6
2Take it away from 1.
1−0.4=0.6

The probability it rains tomorrow is 0.3. Work out the probability it does not rain.

1Shade what you know.
whole = 10.30.7
2Take it away from 1.
1−0.3=0.7
1what you knowleft21−what you know=left

The probability Ava does not win a prize is 0.8. Work out the probability she wins a prize.

1Shade what you know.
whole = 10.80.2
2Take it away from 1.
1−0.8=0.2

1what you knowleft21−what you know=left

1The probability a dog barks at the door is 0.9. Work out the probability it does not bark.

1Shade what you know.
whole = 10.90.1
2Take it away from 1.
1−0.9=0.1

2The probability Leo is late is 0.1. Work out the probability he is not late.

1Shade what you know.
whole = 10.10.9
2Take it away from 1.
1−0.1=0.9

3The probability a bus is not full is 0.6. Work out the probability it is full.

1Shade what you know.
whole = 10.60.4
2Take it away from 1.
1−0.6=0.4

4The probability a team wins is 25. Work out the probability it does not win.

1Shade what you know.
whole = 12535
2Take it away from 1.
1−25=35

How much of the whole bar is shaded?

whole = 10.30.40.3 + 0.4 = 0.7
whole = 10.50.10.5 + 0.1 = 0.6
whole = 10.20.20.40.2 + 0.2 + 0.4 = 0.8

whole = 1what you knowleft
what you know+what you know
1−what you know=left
  1. 1Shade what you know.The whole bar is 1.
  2. 2Add what you know.Add up all the outcomes you know.
  3. 3Take it away from 1.What is left is the answer.

Work out the probability of green.

OutcomeRedBlueGreen
Probability0.30.5?
1Shade what you know.
whole = 10.30.50.2
2Add what you know.
0.3+0.5=0.8
3Take it away from 1.
1−0.8=0.2

Work out the probability of C.

OutcomeABC
Probability0.40.1?
1Shade what you know.
whole = 10.40.1?0.5
2Add what you know.
0.4+0.1=0.5
3Take it away from 1.
1−0.5=0.5

Work out the probability of green.

OutcomeRedBlueGreen
Probability0.30.5?
1Shade what you know.
whole = 10.30.50.2
2Add what you know.
0.3+0.5=0.8
3Take it away from 1.
1−0.8=0.2
1what you knowleft2what you know+what you know31−what you know=left

Work out the probability of blue.

OutcomeRedYellowBlue
Probability0.20.6?
1Shade what you know.
whole = 10.20.6?0.2
2Add what you know.
0.2+0.6=0.8
3Take it away from 1.
1−0.8=0.2

Work out the probability of green.

OutcomeRedBlueGreen
Probability0.30.5?
1Shade what you know.
whole = 10.30.50.2
2Add what you know.
0.3+0.5=0.8
3Take it away from 1.
1−0.8=0.2
1what you knowleft2what you know+what you know31−what you know=left

Work out the probability of 3.

Outcome1234
Probability0.20.3?0.1
1Shade what you know.
whole = 10.20.30.1?0.4
2Add what you know.
0.2+0.3+0.1=0.6
3Take it away from 1.
1−0.6=0.4

Work out the probability of green.

OutcomeRedBlueGreen
Probability0.30.5?
1Shade what you know.
whole = 10.30.50.2
2Add what you know.
0.3+0.5=0.8
3Take it away from 1.
1−0.8=0.2
1what you knowleft2what you know+what you know31−what you know=left

Ella picks one counter from a bag. Work out the probability of white.

OutcomeRedBlueWhite
Probability0.10.5?
1Shade what you know.
whole = 10.10.50.4
2Add what you know.
0.1+0.5=0.6
3Take it away from 1.
1−0.6=0.4

Probabilities that add to 1 worksheet, page 1

Probabilities that add to 1 worksheet, page 2

Answer sheet

Is it right?
Thumbs up: right. Thumbs down: wrong.

  1. It rains: 0.4. It does not rain: 0.6.

    Right

  2. Red: 0.5. Blue: 0.2. So green: 0.7.

    Wrong: green is 0.3

  3. Three colours. Each one is 0.3.

    Wrong: they add to 0.9

  4. The bus is late: 0.1. Not late: 0.9.

    Right

  5. Ali wins: 0.6. Ali does not win: 0.6.

    Wrong: they add to 1.2

  1. A spinner lands on red, blue or green. Red is 0.35. Blue is 0.4. Work out the probability of green.

    0.25

  2. A spinner lands on red, blue or green. Green is 0.4. Red and blue are equally likely. Work out the probability of red.

    0.3

  3. The chance of sun is 45%. The chance of cloud is 30%. Rain is the only other outcome. What is the chance of rain?

    25%

  1. Work out the probability of pink.

    RedBluePink
    0.30.3?

    0.4
    1Shade whatyou know.whole = 10.30.3?2Add whatyou know.+=3Take itaway from 1.1−=

  2. Work out the probability of C.

    ABCD
    0.10.3?0.4

    0.2
    1Shade whatyou know.whole = 12Add whatyou know.++=3Take itaway from 1.1−=

  3. A bus is early, on time or late. Early is 0.1. On time is 0.6. Work out the probability the bus is late.

    0.3
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