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An introduction to risk management

Conditional probabilities

If the probability of one outcome is dependent (conditional) on another outcome, the
expected value can be found by multiplying the relevant probabilities together.

Example 2

There is a 60% chance that sales levels will be high ($3 million) in year 1, and
hence a 40% chance that year 1 sales will be low ($1 million).

If sales in year 1 are high, the sales in year 2 will be either $5 million (30%
probability) or $4 million (70% probability).

If sales in year 1 are low, the sales in year 2 will be either $0.5 million (80%
probability) or $1.5 million (20% probability).

Solution

The expected sales in year 1, which should be entered in year 1 of the
investment appraisal, is (0.60 × 3m) + (0.40 × 1m) = $2.2m

Then, the expected sales in year 2, which should be entered in year 2 of the
investment appraisal, is

(0.60×[(0.30×5m) + (0.70×4m)]) + (0.40×[(0.80×0.5m) + (0.20×1.5m)])=
$2.86m

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