Some basics…….. Some basics……. A picture or listing outcomes helps Find the probabilities of throwing: a double a total of 10 a double or a total.

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Presentation transcript:

Some basics…….

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

B/A means B once A has happened

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

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

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

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

Condition <30

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!

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

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 = 0.914 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 = 0.662 i.e. 66.2% The Prior probability of 0.9 is up-dated according to sample state

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

Sub-totals are useful….

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?