Decision Tree/Examples

Examples of Decision Trees

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 $B$.