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Middle Years

12.01 Describing events

Worksheet
Number of events
1

Consider this list of numbers: 2,\, 2,\, 2,\, 3,\, 3,\, 3,\, 4,\, 4,\, 5,\, 5,\, 5,\, 7,\, 7,\, 7,\, 7,\, 9,\, 9

a

How many numbers are in the list?

b

How many numbers are even?

c

Find the difference between the smallest and the largest number.

d

State the number that occurs most frequently.

2

Consider this list of numbers:\,9,\, 3,\, 9,\, 6,\, 5,\, 3,\, 5,\, 6,\, 5,\, 8,\, 2,\, 7

a

Find the difference between the smallest and the largest number.

b

State the number that occurs most frequently.

c

How many numbers are odd and less than 7?

3

A ten-sided die has all the numbers from 1 to 10 printed on different faces:

a

How many faces show an odd number that is also a prime?

b

How many faces show a number that is a multiple of 2 or a multiple of 3, but not both?

4

A twelve-sided die has all the numbers from 1 to 12 printed on different faces:

a

How many faces show an even number that is also a prime?

b

How many faces show a number that is a multiple of 3 or a multiple of 4, but not both?

5

A standard deck of 52 cards is shown:

Find the number of cards that are:

a

Red.

b

A number between 2 and 8 inclusive.

c

Red and have a number between 2 and 8 inclusive.

d

Red or a king.

e

Diamonds with a number printed on them.

f

More than 2 and at most 9.

g

Black or Kings, but not both.

6

These 25 gems have three different cuts - triangular, rectangular, and octagonal.

There are also three colours of gems - amethysts, emeralds, and rubies.

How many gems are:

a

Rectangular

b

Not octagonal

c

Triangular or octogonal

Mutually exclusive and complementary events
7

Determine whether the following statements are true or false.

a

All complementary events are mutually exclusive.

b

All mutually exclusive events are complementary.

8

Determine whether the following scenarios involve mutually exculsive events:

a

A spinner has the numbers 1 \text{ to } 10. Josh spins the number 4 and then spinning number 7 on the same spinner.

b

A book contains 100 pages. You open to a random page. The page number is 45 or 90.

9

A box of cupcakes contains six chocolate cakes and four cheese cakes. Two of the chocolate cakes and three of the cheese cakes have vanilla filling inside.

a
Is choosing a chocolate cake or choosing a cheese cake mutually exclusive? Explain your answer.
b
Is choosing a chocolate cake and choosing a cake with vanilla icing mutually exclusive? Explain your answer.
10

For each of the following, state whether the two events are complementary:

a
  • Event 1: Selecting a positive number.

  • Event 2: Selecting a negative number.

b
  • Event 1: Drawing a red card from a standard deck of cards (no jokers).

  • Event 2: Drawing a black card from a standard deck of cards (no jokers).

c
  • Event 1: Drawing a club from a standard deck of cards (no jokers).

  • Event 2: Drawing a spade from a standard deck of cards (no jokers).

d
  • Event 1: Rolling a number greater than 3 on a die.

  • Event 2: Rolling a number less than 3 on a die.

11

For each of the following pair of events determine whether they are:

i

Mutually exclusive

ii

Complementary

a
  • Event 1: A six-sided die is rolled, and the result is a 2

  • Event 2: A six-sided die is rolled, and the result is an odd number

b
  • Event 1: A six-sided die is rolled, and the result is 3 or less

  • Event 2: A six-sided die is rolled, and the result is 4 or more

c
  • Event 1: A six-sided die is rolled, and the result is more than 2

  • Event 2: A six-sided die is rolled, and the result is less than 3

d
  • Event 1: A six-sided die is rolled, and the result is factor of 6

  • Event 2: A six-sided die is rolled, and the result is a 2

12

Consider the following events:

  • Event 1: A six-sided die is rolled, and the result is a factor of 12

  • Event 2: A six-sided die is rolled, and the result is a 1

  • Event 3: A six-sided die is rolled, and the result is 5 or more

a

Are Event 1 and Event 2 mutually exclusive?

b

Are Event 1 and Event 3 mutually exclusive?

c

Are Event 2 and Event 3 mutually exclusive?

d

Is there a pair of complementary events? If yes, state the complementary events.

13

A constellation is randomly selected from the following six constellations:

Consider the following events:

  • Event 1: The constellation has 7 or more stars

  • Event 2: The constellation has more than 4 stars

  • Event 3: The name of the constellation begins with a C

  • Event 4: The name of the constellation begins with a consonant

Which two events are mutually exclusive?

14

A constellation is randomly selected from the following six constellations:

Consider the following events:

  • Event 1: The name of the constellation begins with a consonant

  • Event 2: The constellation has an even number of stars

  • Event 3: The constellation has less than 5 stars

  • Event 4: The name of the constellation has more than 6 letters

Which two events are complementary?

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