1. Statistics
Probability

2. Conditional Probability: multiplication rule
KUS objectives
BAT apply the multiplication rule for conditional probabilities
Starter: A

3. WB 9 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.
A UK
B France
VENN
DIAGRAM of UK - France 9 23 2 56
A tourist is chosen from the people with French passports. What is the probability they also have a British passport?
A tourist is chosen from the people with British passports. What is the probability they also have a French passport?

4. Notes Conditional probability
VENN
DIAGRAM

5. WB 10
X low
Y high
The people backstage at a concert are given one or both of two types of security pass. Type X and type Y. The numbers of passes given out are shown in the diagram
A security check stops each person that enters or leaves. What is: 46 9 15
VENN DIAGRAM X Y X Y Y X

6. Given that P(X) = 0.6 P(Y) = 0.4 and P(X  Y) = 0.8 Find:
WB 11
Given that P(X) = P(Y) = and P(X  Y) = 0.8
Find:
Addition law: X Y
0.4
0.2
Multiplication law:
Multiplication law:

7. A B 0.15 0.2 Given that P(A) = 0.6 P(B') = 0.65 and P(A  B) = 0.15
WB 12
Given that P(A) = P(B') = and P(A  B) = 0.15
Find A B
0.45
0.15
0.2
Addition law:
Multiplication law:
Venn Diagram
Multiplication law:

8. DIAGRAM for conditional probability
Notes THE MULTIPLICATION RULE
P(A/B) A B
P(B)
TREE
DIAGRAM for conditional probability A’ A B’ A’

9. 8 15 1 2 4 X = 1 2 Green 8 15 Green 1 2 8 15 1 2 4 X = Red 4 7 Green 7
WB 13
Adam has 8 green balls and 7 red balls in a bag. He takes out two balls without replacement. 8 15 1 2 4 X = 1 2
Green 8 15
Green 1 2 8 15 1 2 4 X =
Red 4 7
Green 7 15 4 X = 7 15
Red 3 7 7 15 3 X =
Red
a) What is P (Red  Red) ?
b) What is P (2nd is red / 1st is red) ?

10. WB 14 An athlete swims or runs each morning in the ratio 3:4
WB 14 An athlete swims or runs each morning in the ratio 3:4. If she swims then she spends time in the gym with probability If she runs she spends time in the gym with probability 0.85
Represent this information on a tree diagram
Find the probability that on any particular day he uses the Gym
Given that she did not use the Gym one day, what is the probability that she went swimming that day 3 7 9 20 27
140 X = 11 33 4 17 68 12 b)
Gym
Swim
Run
No Gym 3 7 9 20 17 4 11 a) c)

11. WB 15 Biologists have studied polecats breeding in the wild with the following results. 35% of polecats carry an intestinal disease. The probability that a female pole cat will conceive given that it has the disease is 0.67 and if it does not the probability is 0.92
Draw a tree diagram
Find the Probability that a Female polecat conceives given that it has the disease
Find the Probability that a Female polecat conceives and that it has the disease
Given that a Polecat has conceived what is the probability it was disease free?
Conceive
Disease No
Not a)
0.35
0.65
0.35 x 0.33 =
0.35 x 0.67 =
0.67
0.92
0.33
0.08
0.65 x 0.92 = 0.598
0.65 x 0.08 = 0.052
b) !!! c) d)

12. If two events are independent
Notes INDEPENDENT EVENTS
If two events are independent
How will this affect the formulas for probabilities?
(Not a conditional probability )
Exam questions often ask you to decide if events are independent
Use the formulas highlighted to answer

13. The events A and B are independent such that
WB 16
The events A and B are independent such that
a) Find the value of x
For this value of x find b) c)

14. One thing to improve is –
KUS objectives
self-assess
One thing learned is –
One thing to improve is –

15. END