The managers of a car dealership are trying to determine the

The managers of a car dealership are trying to determine the effect on their sales of their arch rival’s advertising campaign. They collected data on sales which show the following result:

low

medium

high

days

Rival advertises

48

16

22

86

Doesn’t advertise

56

20

32

108

Total

104

36

54

194

         With reference to the above determine the following probabilities:

(i)        p(next week’s sales will be high)

(ii)       p(next week’s sales will be high | the competitor advertises)

(iii)      p(next week’s sales will be high | the competitor does not advertise)

(iv)      p(next week’s sales will be low)

(v)       p(next week’s sales will be low | the competitor advertises).

(b)    Do the events ‘competitor advertises’ and ‘high sales’ appear to be independent?

Solution

i)

P(high) = 54/194 = 0.278350515 [ANSWER]

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ii)

P(high|adv) = 22/54 = 0.407407407 [ANSWER]

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iii)

P(high|not adv) = 32/54 = 0.592592593 [ANSWER]

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iv)

P(low) = 104/194 = 0.536082474 [ANSWER]

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v)

P(low|adv) = 48/104 = 0.461538462 [ANSWER]

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b)

As

P(high) =/= P(high|adv) [parts i and ii]

Then THEY ARE NOT INDEPENDENT.