Probability testing Company X sells one product codenamed A1. The marketing department has estimated that the sales of A1 for a forthcoming budget period could be £1000, £1500 or £2000. On further investigation it would appear that there is a 70 per cent chance that the sales will be £1000,

Question

Probability testing

Company X sells one product codenamed A1. The marketing department has estimated that the sales of A1 for a forthcoming budget period could be £1000, £1500 or £2000. On further investigation it would appear that there is a 70 per cent chance that the sales will be £1000, a 20 per cent chance that the sales will be £1500 and a 10 per cent chance that the sales will be £2000.

Required:
Calculate the expected value of sales for product A1 during the forthcoming budget period.

Accepted Answer

The question requires us to calculate the expected value of the sales of A1 for the forthcoming period. It might be easier for you to think of the expected value as the weighted average, which perhaps provides a clue to what is required. In order to calculate the expected values the budgeted sales figures are multiplied by their respective chances or probabilities. So:

Budgeted sales (1)	Probability (2)	Expected value (3)
£	%	£
1 000	70	700
1 500	20	300
2 000	[latex]\underline{10} [/latex]	[latex]\underline{200} [/latex]
[latex]\underline{\underline{100} }[/latex]		[latex]\underline{\underline{1 200} }[/latex]

Tutorial notes

1 The expected value (or weighted average) of the sales for the forthcoming budget period is £1200 [as per column (3).]

2 The answer has been obtained by multiplying the three estimated levels of sales by their respective probabilities (column (1) multiplied by column (2)).

3 In this exhibit, the probabilities are expressed in percentage terms. When combined, they should always total 100%. Note that sometimes they are expressed in decimal terms; they should then total 1.0 (in our example 0.7 + 0.2 + 0.1 = 1.0).

4 The probabilities are estimates. They may be made partly on past experience, partly on an investigation of the market and partly on instinct. In other words they might be better described as ‘guesstimates’.

5 Does the solution make sense? The expected value is £1200; this is £200 more than the lowest level of sales of £1000; the probability of this level being achieved is 70 per cent. The chance of the sales being at least £1000 is quite high. By contrast, there is only a 20 per cent probability that the sales could be as high as £1500 and only a 10 per cent chance that they could reach £2000. It seems reasonable to assume, therefore, that the sales are likely to be nearer £1000 than £1500 and that £1200 appears to be a reasonable compromise.

Question 18.1: Probability testing Company X sells one product codenamed A1...

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