12.01 Describing events
Consider this list of numbers: 2,\, 2,\, 2,\, 3,\, 3,\, 3,\, 4,\, 4,\, 5,\, 5,\, 5,\, 7,\, 7,\, 7,\, 7,\, 9,\, 9
How many numbers are in the list?
How many numbers are even?
Find the difference between the smallest and the largest number.
State the number that occurs most frequently.
Consider this list of numbers:\,9,\, 3,\, 9,\, 6,\, 5,\, 3,\, 5,\, 6,\, 5,\, 8,\, 2,\, 7
Find the difference between the smallest and the largest number.
State the number that occurs most frequently.
How many numbers are odd and less than 7?
A ten-sided die has all the numbers from 1 to 10 printed on different faces:
How many faces show an odd number that is also a prime?
How many faces show a number that is a multiple of 2 or a multiple of 3, but not both?
A twelve-sided die has all the numbers from 1 to 12 printed on different faces:
How many faces show an even number that is also a prime?
How many faces show a number that is a multiple of 3 or a multiple of 4, but not both?
A standard deck of 52 cards is shown:
Find the number of cards that are:
Red.
A number between 2 and 8 inclusive.
Red and have a number between 2 and 8 inclusive.
Red or a king.
Diamonds with a number printed on them.
More than 2 and at most 9.
Black or Kings, but not both.
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:
Rectangular
Not octagonal
Triangular or octogonal
Determine whether the following statements are true or false.
All complementary events are mutually exclusive.
All mutually exclusive events are complementary.
Determine whether the following scenarios involve mutually exculsive events:
A spinner has the numbers 1 \text{ to } 10. Josh spins the number 4 and then spinning number 7 on the same spinner.
A book contains 100 pages. You open to a random page. The page number is 45 or 90.
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.
For each of the following, state whether the two events are complementary:
Event 1: Selecting a positive number.
Event 2: Selecting a negative number.
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).
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).
Event 1: Rolling a number greater than 3 on a die.
Event 2: Rolling a number less than 3 on a die.
For each of the following pair of events determine whether they are:
Mutually exclusive
Complementary
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
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
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
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
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
Are Event 1 and Event 2 mutually exclusive?
Are Event 1 and Event 3 mutually exclusive?
Are Event 2 and Event 3 mutually exclusive?
Is there a pair of complementary events? If yes, state the complementary events.
A constellation is randomly selected from the following six constellations:
Consider the following events:
Event 1: The constellation has 7 or more stars
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Event 2: The constellation has more than 4 stars
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Event 3: The name of the constellation begins with a C
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Event 4: The name of the constellation begins with a consonant
Which two events are mutually exclusive?
A constellation is randomly selected from the following six constellations:
Consider the following events:
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Event 1: The name of the constellation begins with a consonant
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Event 2: The constellation has an even number of stars
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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?
