2. Some basics…….

4. A picture or listing outcomes helps
Find the probabilities of throwing:
a double
a total of 10
a double or a total of 10
at least one 6

6. B/A means B once A has happened

7. 1. If a ball is selected and then replaced… Events are independent
3 white and 7 blue balls in a bag
1. If a ball is selected and then replaced… w w b w b b
Events are independent

8. 1. If a ball is selected and then replaced… Events are independent
3 white and 7 blue balls in a bag
1. If a ball is selected and then replaced…
WW = 3/10 x 3/10 = 9/100
3/10 w w
3/10
7/10 b
3/10 w
7/10 b
7/10 b
Events are independent

9. 2. If a ball is selected but not replaced…
2/9
WW = 3/10 x 2/9 = 6/90 w w
3/10
7/9 b
3/9 w
7/10 b
6/9 b
Events are dependent

10. involve two classifications
The results of a survey of 250 customers at a jeans store
can help us in marketing:
MARGINAL PROBABILITIES
are found on edge of table
P(F) = 100/250 = 0.4
JOINT PROBABILITIES
involve two classifications
P( M and 30+) = 50/250 = 0.2

11. Condition
<30

14. Prob of A after B has happened
Prob A * conditional prob of B after A has happened
Total prob of B
Do not panic!
The formula you find in text books look complicated but using a tree diagram is straightforward and gives the same answer!

16. Conditional probs
P(ND/C)
.95 nd
=0.855 c .9 ND
.05 d
=0.045
0.935 .8 nd
=0.08 .1 D nc
0.065 .2 d
=0.02

17. Sampling:
If you pick out a non-defective item, the probability of the process being in control is:
P(C/ND) = 0.855/0.935 = i.e. 91.4%
If you pick out a defective item, the probability of the process being in control is:
P(C/D) = 0.045/0.068 = i.e. 66.2%
The Prior probability of 0.9 is up-dated according to sample state

18. Analyse the following data using different probabilities.
What is the relationship between age, dress and buying behaviour?

20. Sub-totals are useful….

21. The following information comes from the same store, but for male buyers.
Analyse the data using a tree diagram and Bayes.
Who should the shop assistant target?