Decision Tree/Examples/Arbitrary Example 1
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Example of Decision Tree
Consider the case of a builder who is allowed to tender for only one of two contracts.
If he tenders for contract $A$, there is a $70 \%$ probability of winning the contract, and thereby making a profit of $\$10\,000$.
If he tenders for contract $B$, there is only a $20 \%$ probability of winning the contract, but his profit will be $\$30\,000$.
If he fails to win either contract, he will do other work instead and make a profit of $\$5000$.
The decision tree for making the decision as to which contract to bid for is shown here:
Here, the expected gains for contracts $A$ and $B$ are calculated as follows:
- For contract $A$: $\$10\,000 \times 0.7 + \$5000 \times 0.3 = \$8500$
- For contract $B$: $\$30\,000 \times 0.2 + \$5000 \times 0.8 = \$10\,000$
Hence, for a maximum expected gain, the builder should tender for contract $B$.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): decision tree
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): decision tree