PROBABILITY - Text version of PowerPoint slides (minus the graphics!)

 

Slides 3,4,12,18,21 containing questions to be answered.

 

 

Slide 3

 

RULES OF ADDITION

If events are exclusive:

Prob (A or B) = P(A u B)

= P(A) + P(B)

P( 1 or 6 ) = P (K or Q) =

If events are not exclusive:

P( A u B) = P(A) + P(B) - P(A n B)

 

Question 3.1:  P(Heart or Queen) =

 

 

Question 3.2:  P(Spade or Picture) =

 

Slide 4

 

A picture or listing outcomes helps

 

Investigate throwing two dice and

adding the totals:

How many possible outcomes are

there?

6 . . . . . .

5 . . . . . .

4 . . . . . .

3 . . . . . .

2 . . . . . .

1 . . . . . .

1 2 3 4 5 6

 

Find the probabilities of throwing:

Question 4.1:  • a double

 

Question 4.2:  • a total of 10

 

Question 4.3:  • a double or a total of 10

 

Question 4.4:  • at least one 6

 

 

 

Slide 12

 

 

Find the percentage or probability give information about the customers and underlying trends: 

conditional probabilities look for a pattern:

age versus gender

e.g. P(30+/ F) and P(30+/M)

or P(F/<30) and P(M/<30)

Age Male Female totals

< 30 100 75 175

30+ 50 25 75

totals 150 100 250

 

 

 

Question: 12.1  work out probabilities of age or gender profile P(30+); P(F)

 

 

Question: 12.2  work out probabilities P(30+/ F) and P(30+/M)

 

 

Question: 12.3  work out probabilities of P(F/<30) and P(M/<30)

 

 

 

 

 

Slide 18

 

Analyse the following data using different probabilities.

What is the relationship between age, dress and buying

behaviour?

A probability case study based on actual data in USA

· 12 Up - market fashion stores selling women clothing.

· These attract many window shoppers and tourists.

· It would be useful if staff could identify serious buyers.

· The Market Research thinks that buying pattern is affected by age and dress of
  the shoppers.

 

 

Question:  Work out the probabilities (percentages) of:

 

            <40 well-dressed buyers

            40+ well-dressed buyers

            <40 casual buyers

            40+ casual buyers

            <40 well-dressed non-buyers

            40+ well-dressed non-buyers

            <40 casual non-buyers

            40+ casual non-buyers

 

            Percentages should add up to 100%.

 

 

Slide 21

 

The following information comes from the same store, but for male buyers.

 

Question: Analyse the data using a tree diagram and calculating probabilities.

Who should the shop assistant target?

 

Male buyers

· form 1/3rd  of customers

· 6 out of 10 made a purchase

· of those who made a purchase 2 out of 10 wore suits

· of those who didn't make a purchase 9 out of 10 were not in a suit

 

 

 

 

Hint:  probabilities should add up to 0.333 (i.e. 1/3rd of customers)

 

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