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Question

Probabilities for three states of the economy and probabilities for the returns on a particular stock in each state are shown in the table below.

Probability of StockProbability of       StockPerformance in GivenState of EconomyEconomic StatePerformanceEconomic StateGood.3Good.6Neutral.3Poor.1Neutral.5Good.4Neutral.3Poor.3Poor.2Good.2Neutral.3Poor.5\begin{array}{lclc}\hline &&&\textbf{Probability of Stock}\\ &\textbf{Probability of}&\textbf{~~~~~~~Stock}&\textbf{Performance in Given}\\ \textbf{State of Economy}&\textbf{Economic State}&\textbf{Performance}&\textbf{Economic State}\\\hline \text{Good}&.3&\text{Good}&.6\\ &&\text{Neutral}&.3\\ &&\text{Poor}&.1\\\hline \text{Neutral}&.5&\text{Good}&.4\\ &&\text{Neutral}&.3\\ &&\text{Poor}&.3\\\hline \text{Poor}&.2&\text{Good}&.2\\ &&\text{Neutral}&.3\\ &&\text{Poor}&.5\\\hline \end{array}

What is the probability that the economy will be neutral and the stock will experience poor performance?

Solution

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In order to determine the probability of both of these things happening at the same time we need to multiply the probability of a neutral economy (.5) by the probability of a poor stock performance in a neutral economy (.3).

.3 X .5 = .15 or 15%

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