1. Probability

2. Some fundamentals 𝑨 2 4 6 3 5 1 𝑩 𝑺
𝑆= the whole sample space (1 to 6)
𝐴= even number on a die thrown
𝐵= prime number on a die thrown
What does it mean in this context?
What is the resulting set of outcomes? 𝐴′ ?
Not A.
i.e. Not rolling an even number. ?
{1, 3, 5}
𝐴∪𝐵 ?
A or B. i.e. Rolling an even or prime number. ?
{2,3,4,5,6}
𝐴∩𝐵 ?
A and B. i.e. Rolling a number which is even and prime. ?
{2}

3. Some fundamentals 𝑨 2 4 6 3 5 1 𝑩 𝑺
𝑆= the whole sample space (1 to 6)
𝐴= even number on a die thrown
𝐵= prime number on a die thrown
What does it mean in this context?
What is the resulting set of outcomes?
𝐴∩𝐵′ ?
Rolling a number which is even and not prime. ?
{4,6}
(𝐴∪𝐵)′ ?
Rolling a number which is not [even or prime]. ?
{1}
𝐴∩𝐵 ′ ?
Rolling a number which is not [even and prime]. ?
{1,3,4,5,6}

4. What area is indicated? A C B S
𝐴∩𝐵 ?

5. What area is indicated? A C B S
𝐴∪𝐵 ?

6. What area is indicated? A C B S
𝐴∩𝐵∩𝐶 ?

7. What area is indicated? A C B S
𝐴∩ 𝐶 ′ ?

8. What area is indicated? A C B S
𝐴∩𝐵∩ 𝐶 ′ ?

9. A C B S 𝐴 ′ ∩ 𝐵 ′ ∩ 𝐶 ′ 𝐴∪𝐵∪𝐶 ′ What area is indicated? ? ? or
alternatively… ?
𝐴∪𝐵∪𝐶 ′

10. What area is indicated? A C B S
𝐴 ′ ?

11. What area is indicated? A C B S
𝐴∩ 𝐵∩𝐶 ′ ?

12. What area is indicated? A C B S
𝐴∩ 𝐵 ′ ∩𝐶′ ?

13. Test Your Understanding? 𝑆 𝐵 𝐴
0.33
0.32
0.3
0.05
Given that 𝑃 𝐴 ′ ∩𝐵 =0.3 and 𝑃 [𝐴∪𝐵]′ =0.05 and 𝑃 𝐵 =0.62, determine: (using a suitable Venn Diagram)
𝑃 𝐴 =𝟎.𝟔𝟓 𝑃 𝐴∩𝐵 =𝟎.𝟑𝟐 𝑃 𝐴∩𝐵′ =𝟎.𝟑𝟑 𝑃 𝐴∪𝐵 =𝟎.𝟗𝟓 ? a b ? c ? d ?

14. Probability Formulae from the Venn Diagram – The Addition Rule
A and B are two events such that P(A) = 0.6, P(B) = 0.7 and P(A or B) = 0.9.
Calculate: a) b) c) d) a) S A B
0.2
0.4
0.3
0.1
Now you know the intersection, you can draw a Venn diagram! 5C

15. Probability Formulae from the Venn Diagram – The Addition Rule
A and B are two events such that P(A) = 0.6, P(B) = 0.7 and P(A or B) = 0.9.
Calculate: b) c) d) b) S A B
0.2
0.4
0.3
‘Probability of not A’
0.1
‘Probability of not A, or B’
‘Probability of not A, and B’ 5C