1. Introduction to Probability
AS Maths with Liz
Stats 1

2. What is probability?
Probability is the likelihood or chance of an event happening.
Probability Scale
Probability cannot be above 1 (100%).
Formula:

3. Notation Let A and B represent two separate events.
Note: Probabilities always add up to 1.
Which leads to…

4. Example 1
Let E represent rolling an even number on an unbiased 6 sided dice. Find (a) (b) (c)

5. Example 2
If a member is picked at random, what is (a) P(12 year old boy) (b) P(girl) If a girl is picked at random, what is (c) P(13 years old) If a 13 year old is picked at random, what is (d) P(boy)

6. Example 3
At a school sports day, 200 students took part in various events. 76 students did track events, 11 did both track and field events, and 72 did neither. Let T be the event that a student did track, and let F be the event that a student did field.
Work out the following and put your results in the table:
(a)
(b)
(c)
(d)
Work out
(e)
(f)
(g)
(h)

7. Key terms
A set of events are independent if the outcome of one has no effect on the outcome of the other.
Example: Tossing a coin and landing on heads and rolling a 5 on a die.
A set of events are mutually exclusive if they cannot both happen at the same time.
Example: Choosing a card and ending up with an Ace and King.
A set of events are non-mutually exclusive if they can both happen at once.
Example: Choosing a card and ending up with a King and a Heart
A set of events is exhaustive if they cover all the possible outcomes.

8. The AND rule
If we consider the possibility of two successive independent events both occurring, we multiply their probabilities.
Example: A coin is flipped at the same time as a dice is rolled. Find the probability of obtaining a head and a 5.
If A and B are mutually exclusive events, then

9. The OR rule
If we consider the possibility of one event OR the other occurring successively, we add their probabilities and take away the overlap.
Note: If the two events are mutually exclusive, there will be no overlap.

10. Q1 from handout

11. Q2 from handout

12. Q3 You try!

13. Q4 You try!

14. Q5 – You try

15. Q6

16. Q7

17. Independent Study FINISH TREE DIAGRAM questions on handout
Mymaths – Probability Introduction
Mymaths – Venn Diagrams
Stats Textbook – Pg. 39, Exercise 2A
DUE FRIDAY FEBRUARY 6TH