Question

Describe the difference between a probability derived from the analytic view (logical analysis), the Relative Frequency view (sampling from a distribution with known characteristics), and the Subjective (feeling) view. Describe situations in which each view of probability could be useful.

Answer 1

1) Objective Probability :

Objective probability refers to the chances or the odds that an event will occur based on the analysis of concrete measures rather than hunches or guesswork. Each measure is a recorded observation, a hard fact, or part of a long history of collected data. The probability estimate is computed using mathematical equations that manipulate the data to determine the likelihood of an independent event occurring. An independent event is an event whose outcome is not influenced by prior events. Subjective probability, by contrast, may utilize some method of data analysis but also uses guesstimates or intuition to determine the chances of a specific outcome.

Examples of Objective Probability :

One could determine the objective probability that a coin will land "heads" up by flipping it 100 times and recording each observation. This would likely yield an observation that the coin landed on "heads" approximately 50% of the time, which is an example of a purely objective probability.

• Objective probability is the probability an event will occur based on an analysis in which each measure is based on a recorded observation or a long history of collected data.
• In contrast, subjective probability allows the observer to gain insight by referencing things they've learned and their own experience.
• In finance, people ought to use objective probabilities to make decisions instead of relying on subjective stories, personal experience, or anecdotal evidence.

2) Subjective Probability :

Subjective probability is a type of probability derived from an individual's personal judgment or own experience about whether a specific outcome is likely to occur. It contains no formal calculations and only reflects the subject's opinions and past experience. Subjective probabilities differ from person to person and contain a high degree of personal bias. An example of subjective probability is a "gut instinct" when making a trade.

Subjective probability can be contrasted with objective probability, which is the computed probability that an event will occur based on an analysis in which each measure is based on a recorded observation or a long history of collected data.

Examples of Subjective Probability :

An example of subjective probability is asking New York Yankees fans, before the baseball season starts, about the chances of New York winning the World Series. While there is no absolute mathematical proof behind the answer to the example, fans might still reply in actual percentage terms, such as the Yankees having a 25% chance of winning the World Series.

In another scenario, consider a person who is asked to predict the percentage chance of whether a flipped coin will land with heads or tails up, his initial response may be the mathematically true 50%. If 10 coin flips occur, all resulting in the coin landing tails up, the person may change his percentage chance to a number other than 50%, such as saying the chance of it landing tails up is 75%. Even knowing that the new prediction is mathematically inaccurate, the individual’s personal experience of the previous 10 coin flips has created a situation in which he chooses to use subjective probability.

• Subjective probability is a type of probability derived from an individual's personal judgment or own experience about whether a specific outcome is likely to occur.
• It contains no formal calculations and only reflects the subject's opinions and past experience rather than on data or computation.
• Subjective probabilities differ from person to person and contain a high degree of personal bias.

Objective vs. Subjective Probability :

Objective probabilities are a more accurate way to determine the probability of a given outcome than subjective probability That's because subjective probability is largely based on human judgment and experiences. Objective probability, on the other hand, allows the observer to gain insight from historical data and then assess the likelihood of a given outcome.