Venn diagrams and probability

The Maths Habit

Where does each shape go?

Has 4 sidesShaded

Work these out.

3 + 2 + 4 + 1105 + 1 + 2 + 6144 + 3 + 7 + 2163 red, 4 blue. P(red)?37

Venn diagram
Circles in a box that sort things into groups. Everyone is somewhere in the box.
ξAB
Both
In both circles: the middle.
ξAB
Only
In one circle, not the middle.
ξAB
Neither
In no circle: outside the circles, in the box.
ξAB
At random
Without looking, so each one has the same chance.

ξAB4231
1all2ones you want3
P(both) =ones you wantall
  1. 1Add all the numbers.The one outside too. This goes on the bottom.
  2. 2Find the ones you want.Shade them. This goes on the top.
  3. 3Write the fraction.Put the top over the bottom.

One person is picked at random. Find P(both).

ξAppleBanana2341
1Add all the numbers.
2 + 3 + 4 + 1 =10
2Find the ones you want.
3
3Write the fraction.
P(both) =310in the middleall

One person is picked at random. Find P(neither).

ξPenPencil5132
1Add all the numbers.
5 + 1 + 3 + 2 =11
2Find the ones you want.
2
3Write the fraction.
P(neither) =211outside the circlesall

One person is picked at random. Find P(both).

ξAppleBanana2341
1Add all the numbers.
2 + 3 + 4 + 1 =10
2Find the ones you want.
3
3Write the fraction.
P(both) =310in the middleall
1Add all the numbers.2Find the ones you want.3Write the fraction.

One person is picked at random. Find P(dance only).

ξSingDance3242
1Add all the numbers.
3 + 2 + 4 + 2 =11
2Find the ones you want.
4
3Write the fraction.
P(dance only) =411only in Danceall

One person is picked at random. Find P(both).

ξAppleBanana2341
1Add all the numbers.
2 + 3 + 4 + 1 =10
2Find the ones you want.
3
3Write the fraction.
P(both) =310in the middleall
1Add all the numbers.2Find the ones you want.3Write the fraction.

One person is picked at random. Find P(both).

ξBusWalk4153
1Add all the numbers.
4 + 1 + 5 + 3 =13
2Find the ones you want.
1
3Write the fraction.
P(both) =113in the middleall

One person is picked at random. Find P(both).

ξAppleBanana2341
1Add all the numbers.
2 + 3 + 4 + 1 =10
2Find the ones you want.
3
3Write the fraction.
P(both) =310in the middleall
1Add all the numbers.2Find the ones you want.3Write the fraction.

One student is picked at random. Find P(neither).

ξMathsPE6214
1Add all the numbers.
6 + 2 + 1 + 4 =13
2Find the ones you want.
4
3Write the fraction.
P(neither) =413outside the circlesall

1Add all the numbers.2Find the ones you want.3Write the fraction.

1Find P(both).

ξCatsDogs2143
1Add all the numbers.
2 + 1 + 4 + 3 =10
2Find the ones you want.
1
3Write the fraction.
P(both) =110in the middleall

2Find P(tea only).

ξTeaMilk3422
1Add all the numbers.
3 + 4 + 2 + 2 =11
2Find the ones you want.
3
3Write the fraction.
P(tea only) =311only in Teaall

3Find P(neither).

ξHatCoat5233
1Add all the numbers.
5 + 2 + 3 + 3 =13
2Find the ones you want.
3
3Write the fraction.
P(neither) =313outside the circlesall

One person is picked at random. Find P(football).

ξFootballRugby4322
1Add all the numbers.
4 + 3 + 2 + 2 =11
2Find the ones you want.
4 + 3 =7
3Write the fraction.
P(football) =711in the Football circleall

One person is picked at random. Find P(dance).

ξSingDance2351
1Add all the numbers.
2 + 3 + 5 + 1 =11
2Find the ones you want.
3 + 5 =8
3Write the fraction.
P(dance) =811in the Dance circleall

One person is picked at random. Find P(football).

ξFootballRugby4322
1Add all the numbers.
4 + 3 + 2 + 2 =11
2Find the ones you want.
4 + 3 =7
3Write the fraction.
P(football) =711in the Football circleall
1Add all the numbers.2Find the ones you want.3Write the fraction.

One person is picked at random. Find P(pizza).

ξPizzaChips3244
1Add all the numbers.
3 + 2 + 4 + 4 =13
2Find the ones you want.
3 + 2 =5
3Write the fraction.
P(pizza) =513in the Pizza circleall

One person is picked at random. Find P(football).

ξFootballRugby4322
1Add all the numbers.
4 + 3 + 2 + 2 =11
2Find the ones you want.
4 + 3 =7
3Write the fraction.
P(football) =711in the Football circleall
1Add all the numbers.2Find the ones you want.3Write the fraction.

One person is picked at random. Find P(car).

ξBikeCar1432
1Add all the numbers.
1 + 4 + 3 + 2 =10
2Find the ones you want.
4 + 3 =7
3Write the fraction.
P(car) =710in the Car circleall

One person is picked at random. Find P(football).

ξFootballRugby4322
1Add all the numbers.
4 + 3 + 2 + 2 =11
2Find the ones you want.
4 + 3 =7
3Write the fraction.
P(football) =711in the Football circleall
1Add all the numbers.2Find the ones you want.3Write the fraction.

One person is picked at random. Find P(fruit).

ξCakeFruit2252
1Add all the numbers.
2 + 2 + 5 + 2 =11
2Find the ones you want.
2 + 5 =7
3Write the fraction.
P(fruit) =711in the Fruit circleall

Venn diagrams and probability worksheet, page 1

Venn diagrams and probability worksheet, page 2

Answer sheet

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

ξRedBlue6234

  1. P(both) = 215

    Right

  2. P(neither) = 411

    Wrong: the bottom is all 15

  3. P(red only) = 615

    Right

  4. P(red) = 615

    Wrong: the top is 6 + 2 = 8

  5. P(blue only) = 315

    Right

  1. 30 students: 17 play chess, 12 play draughts, 5 play both. Draw the Venn diagram.

    12, 5, 7, 6

  2. Find P(plays exactly one of the games).

    1930

  3. Find P(plays neither). Simplify it.

    630 = 15

  1. One person is picked at random. Find P(both).

    310
    ξTeaMilk43211All102Both3P(both) =

  2. One person is picked at random. Find P(juice).

    611
    ξMilkJuice32421All2Juice3P(juice) =

  3. Find P(neither).

    313
    ξCarBike5233
Exit tickets to print