A dam on a river that holds back a water reservoir begins to leak. Engineers say that there is a 10 percent chance of the dam breaking if repairs are not made. This is an example of ________.

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In this question, we are evaluating the type of probability described by the statement about the dam's chance of breaking.
Option 1: subjective probability. The 10 percent chance is an assessment provided by engineers based on judgment, data they have, and their belief about risk, rather than a result derived from long-run frequencies or a universality of equally likely outcomes. This aligns with the notion of subjective probability, which captures personal or expert belief about how likely an event is to occur.
Option 2: basic probability. This term is often used to refer to probability developed from empirical data or combinatorial counting in a straightforward, often frequency-based context. The scenario does not present a clean experimental frequency or a simple combinatorial count, so this label fits less well than subjective probability.
Option 3: classical probability. Classical probability relies on the assumption that all possible outcomes are equally likely, such as flipping a fair coin. The dam scenario does not indicate that outcomes (dam breaks vs. not breaks) are equally probable in a theoretical sense, so this option is not appropriate.
Option 4: expected value. The expected value is a numerical measure used in decision analysis that combines probabilities with outcomes, typically requiring a payoff for each outcome. While the 10% figure could feed into an expected value calculation, the given statement itself is a probability assessment, not a payoff-weighted expectation. Therefore this option does not directly describe the type of probability at issue.

2025-HS1-FIN60003-Business Statistical Modelling-H1 Mid-semester Test Monday Class

A dam on a river that holds back a water reservoir begins to leak. Engineers say that there is a 10 percent chance of the dam breaking if repairs are not made. This is an example of ________.

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