Area 0 (=P(UlS)) 0.1 Unfavourable

Area E (=P(UIW)) 0.7 Unfavourable

Area F (=P(U/N)) 0.9 Unfavourable

Area B (=P(FIW)) 0.3 Favourable

AreaC (=P(F/N)) 0.1 Fa-

Area A (=P(F/S)) 0.9 Favourable

vourable

Similarly the rectangle referring to a weak market is divided into area E (70% of it, because P(U I W) = 0.7) and area B (30% of it, because P(F I W) = 0.3). The rectangle referring to a non-existent market is divided into areas F (90% of it, because P(U I N) = 0.9) and C (10% of it, because P(F I N) = 0.1). In Figures 2.8 and 2.9 probabilities are associated with areas, which can be measured in the usual way by multiplying length by width. Probabilities, including posterior probabilities, can be calculated by considering the area they are represented by: P(Favourable test market)

Total area associated with favourable test Area A + Area B + Area C = (0.9 X 0.4) + (0.3 x 0.4) + (0.1 X 0.2) = 0.5 =

=

P(Unfavourable test market) = Total area associated with unfavourable test = Area D + Area E + Area F =~.lxO.~+~.7xO.~+~.9xO.~ = 0.5

For conditional probabilities the range of possible outcomes is limited by the condition. In other words there is a preliminary restriction to a subsection of the whole square. A conditional probability is given, therefore, not by the area representing the event, but by this area as a proportion of the area that represents the condition. For P(strong demand given a favourable test market) the preliminary restriction is to the parts of the square relating to a favourable test market (areas A, B and C). P(S I F) is then calculated as the proportion of A + B + C that is associated with a strong demand:

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of it, because P(U I W) = 0.7) and area B (30% of it, because P(F I W) = 0.3). The because P(U I N) = 0.9) and C (10% of it, because P(F I N...

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of it, because P(U I W) = 0.7) and area B (30% of it, because P(F I W) = 0.3). The because P(U I N) = 0.9) and C (10% of it, because P(F I N...