Key difference: Risk is essentially the level of possibility that an action or activity will lead to lead to a loss or to an undesired outcome. The risk may even pay off and not lead to a loss, it may lead to a gain. A probability, on the other hand, is a measure or estimation of how likely is it that an event will come to pass, or that a statement is true. In relation to risk, probability is used to figure out the chance that taking a risk will pay off.

Risk is essentially the level of possibility that an action or activity will lead to lead to a loss or to an undesired outcome. The risk may even pay off and not lead to a loss, it may lead to a gain.

Dictionary.com defines risk as:

• Exposure to the chance of injury or loss; a hazard or dangerous chance: It's not worth the risk.
• The hazard or chance of loss.
• The degree of probability of such loss.
• The amount that the insurance company may lose.
• A person or thing with reference to the hazard involved in insuring him, her, or it.
• The type of loss, as life, fire, marine disaster, or earthquake, against which an insurance policy is drawn.

There are many difference kinds of risk. Wikipedia lists six different ways that risk can be defined:

• A probability or threat of damage, injury, liability, loss, or any other negative occurrence that is caused by external or internal vulnerabilities, and that may be avoided through preemptive action.
• Finance: The probability that an actual return on an investment will be lower than the expected return.
• Food industry: The possibility that due to a certain hazard in food there will be an negative effect to a certain magnitude.
• Insurance: A situation where the probability of a variable (such as burning down of a building) is known but when a mode of occurrence or the actual value of the occurrence (whether the fire will occur at a particular property) is not.
• Securities trading: The probability of a loss or drop in value.
• Workplace: Product of the consequence and probability of a hazardous event or phenomenon.

A probability, on the other hand, is a measure or estimation of how likely is it that an event will come to pass, or that a statement is true. Probabilities are given a value between 0 or 1, where 0 is a 0% chance of the event happening, i.e. it will not happened, and 1 is a 100% chance of the event happening.

Dictionary.com defines probability as:

• The quality or fact of being probable.
• A strong likelihood or chance of something: The probability of the book's success makes us optimistic.
• A probable event, circumstance, etc.: Our going to China is a probability.
• The relative possibility that an event will occur, as expressed by the ratio of the number of actual occurrences to the total number of possible occurrences.
• The relative frequency with which an event occurs or is likely to occur.

Probability is often used in mathematics, statistics, finance, gambling, science, artificial intelligence/machine learning and philosophy. Probability theory is also used to describe the underlying mechanics and regularities of complex systems.

In relation to risk, probability is used to figure out the chance that taking a risk will pay off. If there is a high possibility, i.e. closer to 1, that the risk will pay off, then taking the risk is worth it for the reward. However, if there is a low possibility, i.e. closer to 0, that the risk will pay off, then taking the risk is not worth it, as it will probably result in a loss.

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