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Grade 10 Chapter 12 - Probability Day 15
S = {1, 2, 3, 4, 5, 6}: Sample space
Total outcomes; n(S) = 6
An event is a set of one or more outcomes ex:
A = {to throw an even number on a die} = {2, 4, 6}
Different types of events
Certain events
Probability = 1 (100%)
2 events of equal chance (50/50)
The Probability to get head when a coin is thrown = 50% and the Probability to get tail = 50%
Random events
The Probability to get a 2 on a die = 1
6
Impossible events
The Probability to get an 8 on a die = 0
Elementary and composite events
A = {an even number on a die} = {2, 4, 6} – composite event
B = {a 3 on a die } = {3} – elementary event
Calculation of Probability
P(E) = 𝑎𝑎𝑛𝑡𝑎𝑙 𝑔𝑢𝑛𝑠𝑡𝑖𝑔𝑒 𝑢𝑖𝑡𝑘𝑜𝑚𝑠𝑡𝑒
𝑡𝑜𝑡𝑎𝑙𝑒 𝑎𝑎𝑛𝑡𝑎𝑙 𝑚𝑜𝑜𝑛𝑡𝑙𝑖𝑘𝑒 𝑢𝑖𝑡𝑘𝑜𝑚𝑠𝑡𝑒=
𝑛(𝐸)
𝑛(𝑆)
Example:
Suppose you throw a die. The possible outcomes are: S = {1, 2, 3, 4, 5, 6}
If the event E = {even numbers}= {2, 4, 6}, then
P(E) = 𝑛(𝐸)
𝑛(𝑆)=
3
6=
1
2
Grade 10 Chapter 12 Probability
Grey College 2
Example:
Example:
Grade 10 Chapter 12 Probability
Grey College 3
Exercise 1 p 259 no. a, b, c, f
Grade 10 Chapter 12 Probability
Grey College 4
Day 16
Venn – diagrams
Example:
Union: (OR) The union of C and D is an event, which consist out of all the outcomes from C or D.
C or D = {2; 4; 6; 9; 12}
𝐶 ∪ 𝐷 = {2; 4; 6; 9; 12}
Intersection: (AND) The intersection of C and D is an event, which consist out of the outcomes from C and D.
C and D = {2; 6}
𝐶 ∩ 𝐷 = {2; 6}
Grade 10 Chapter 12 Probability
Grey College 5
Example:
There are no elements which are common. This is mutually exclusive events.
Union: (OR) The union of A and B is:
A or B= {1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12}
𝐴 ∪ 𝐵 = {1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12}
Intersection: (AND) The intersection of A and B is empty:
A and B = { } or ∅
𝐴 ∩ 𝐵 = { } or ∅
Grade 10 Chapter 12 Probability
Grey College 6
Example
Example
Grade 10 Chapter 12 Probability
Grey College 7
Exercise 2 p 262 no. b, f
Grade 10 Chapter 12 Probability
Grey College 8
Exercise 3 p 264 no. a, e
Grade 10 Chapter 12 Probability
Grey College 9
Day 17
Inclusive events:
𝑷(𝑪 𝒐𝒇 𝑫) = 𝑷(𝑪) + 𝑷(𝑫) − 𝑷(𝑪 𝒆𝒏 𝑫)
Mutually exclusive events:
𝑃(𝐴 𝑜𝑓 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) − 𝑃(𝐴 𝑎𝑛𝑑 𝐵) but 𝑃(𝐴 𝑎𝑛𝑑 𝐵) = 0 ∴ 𝑷(𝑨 𝒐𝒇 𝑩) = 𝑷(𝑨) + 𝑷(𝑩)
Grade 10 Chapter 12 Probability
Grey College 10
Grade 10 Chapter 12 Probability
Grey College 11
Exhaustive events: - Two events are exhaustive if together they cover all elements of the sample space.
P(A or B) = 1 Complementary events:
- 2 events are complementary if they are mutually exclusive and exhausted events.
P(A) + P(B) = 1 P( not A) = 1 – P(A)
Grade 10 Chapter 12 Probability
Grey College 12
Example:
Grade 10 Chapter 12 Probability
Grey College 13
Exercise 4 p 269 no. d, e
Exercise 5 p 272 no. a, e, f, g, k
Grade 10 Chapter 12 Probability
Grey College 14
Summary
Union ~ (OR) 𝐴 ∪ 𝐵
Intersection ~ (AND) 𝐴 ∩ 𝐵
Inclusive events
𝑷(𝑪 𝒐𝒇 𝑫) = 𝑷(𝑪) + 𝑷(𝑫) − 𝑷(𝑪 𝒆𝒏 𝑫)
Mutually exclusive events
∴ 𝑷(𝑨 𝒐𝒇 𝑩) = 𝑷(𝑨) + 𝑷(𝑩)
Exhausted events:
P(A or B) = 1 Complementary events:
P(A) + P(B) = 1
