1. Statistics
Probability

2. Probability addition rule
KUS objectives
BAT apply the addition rule for probabilities
Starter: A

3. Where A Intersects B A Union B Notes
A VENN DIAGRAM can show probabilities by arranging numerical information into sets A B
VENN
DIAGRAM
Where A Intersects B A B
A Union B

4. WB 1
In a sample of tourists at an air terminal 87 have only British passports, 15 have american passports, 3 have dual british-american passports and 20 are other nationalities
A UK
B USA
VENN
DIAGRAM of UK - USA 20 15 3 87 B A A B

5. Why is this needed in the formula?
Notes THE ADDITION RULE A B
VENN
DIAGRAM
In the previous example:
P(UK or USA) = P(UK) + P(USA) – P(UK AND USA)
Why is this needed in the formula?

6. WB 2 In a sample of 90 tourists at another air terminal 58 have British passports, 25 have French passports, some have dual british-french passports and 9 are other nationalities.
How many have both French and British passports?
What is the probability of randomly selecting a tourist who only has a French passport?
A UK
B France
VENN
DIAGRAM of UK - France 9 23 2 56 A B =

7. WB 3
A INFO1
B INFO2
A class of 42 AS IT students are entered for resit exams.
Each student takes either the INFO1 exam, INFO2 exam or both
The probability a student takes the INFO 1 exam is
The probability a student took the INFO2 exam is
The probability a student has no resits is
Draw a Venn Diagram
How many students take both exams?

8. 17 20 13 6 14 10 WB 4 A French B Spanish C Italian
A language school offers three courses: Spanish, French or Italian. In July the number of students who enroll is such that :
57% study french
20% study French And Italian
87% study French Or Italian
56% study Spanish
26% study Spanish and Italian
50% study Italian
6% study all three languages
Everyone studies one of these 20 13 10 14 17 6
Draw a Venn Diagram for this situation
A student is chosen at random, what is the probability that they:
Study only Italian?
Study French and Spanish but not Italian?
b) 10%
c) 17%

9. Notes NOTATION A B
NOT B A B
A intersecting NOT B A B A B
NOT (A OR B)

10. WB 5
A Stripes
B Spots
In an aquarium at the zoo 43% of the fish have spots. 8% have both stripes and spots. 28% have neither stripes nor spots.
Find the following Probabilities 29 8 35 28
VENN DIAGRAM of Fish A B A B A B A B

11. WB 6
A Run
B Cycle
Joanne runs or cycles each morning with probabilities as follows:
Draw a Venn Diagram and find the probability that Joanne:
only runs P(run  cycle’)
Does neither P(run’  cycle’)

12. A number is picked randomly from the set of twelve numbers:
A x5+1
B x4+1
C prime
WB 7
A number is picked randomly from the set of twelve numbers:
43, 47
45, 49 40 42 44 48 50 41
46, 51
Todd wants to group the numbers into these sets:
Set A: {one greater than the five x table)
Set B: {one greater than the four x table
Set C: {prime numbers}
Draw a Venn Diagram and put each number in the appropriate space
Find:
P(A  B)
P(A  B  C)
P(B  C’)
Find:
P(A  B  C’)
P(B  C)
P(A’  B’  C’)

13. Notes MUTUALLY EXCLUSIVEB
Events are mutually exclusive if they cannot happen simultaneously or
For example:
The events Pick a Spade and Pick a Heart from a pack of cards are Mutually exclusive
The events David wins the 400m race and Felicity wins the 400m race in the same race are Mutually exclusive (usually)

14. Draw a Venn Diagram and put each number in the appropriate space
WB 8
A primes
C squares
B factors 24
Three events A, B and C can happen in part of a board game. Events A and C are mutually exclusive.
The events depend on the roll of two dice such that players do:
5, 7, 11 10
6, 8, 12
2, 3 9, 4
action A if you roll a prime number
action B if roll a factor of 24
action C if you roll a square number
Draw a Venn Diagram and put each number in the appropriate space
Find these probabilities (be careful of deciding what is a probability):
P(A  B)
P(B  C)
P(A  B’)
Chance of rolling any of 5,7,11,2,3,6,8,12,4
Chance of rolling a 4
Chance of rolling a 5, 7 or 11

15. One thing to improve is –
KUS objectives BAT apply the addition rule for probabilities
self-assess
One thing learned is –
One thing to improve is –

16. END