Aryan -

A prediction is analogous to an estimate of a parameter, but a prediction is for a random variable, the dependent variable, in a regression equation. Thus about a predicted y we have a prediction interval, rather than a confidence interval. An estimated regression coefficient can be shown with a confidence interval around it.

A forecast refers to a time series. But it can also just refer to the future in other contexts.

Note that apparently many people falsely assume that a prediction is necessarily a forecast.

Probability would be the likely occurrence of one or more event(s) in the presence of all possible events.

The two 'scenario' questions you have must be specific to your field.

Cheers - Jim

Prediction is usually a definitive and specific statement about the value of some variable at the specific time in the future.

Forecasting is a probabilistic statement about a range of the possible future values of the variable.

Probability of a specific random event is a chance of the specific event occurring if all relevant events (from the same domain) can be repeated multiple times in the identical stable and uniform conditions.

Note, that there is a axiomatic definition of probability (Kolmogorov) as an inherited property of a random variable, and the frequency of the event occurring in the identical uniform stable conditions is just a quantitative measure of the probability.

Uncertainty (uncertain scenario or factor) is the chance of outcome of the event when multiple observations in the stable uniform conditions are not possible or non-existent. Sometimes it is called subjective probability, i.e. the degree of our belief that the event will occur (not based on frequency of occurring).

For example, a chance of a bridge or building collapse is X [0,1]. It is uncertainty, but not probability. It is based on our knowledge of the various factors and environment related to this object. But it is not possible to repeat collapsing of the same objects multiple times in the same stable and uniform conditions to measure the probability of this event.

All the same!

Perfect explanation from Prof Alexander Kolker , and I may add that in some applications prediction and forecasting are interchangeably used.

Ayman Amin

Agree with you. Indeed, sometimes prediction and forecasting are interchangeably used although they have a different meaning.

Prediction is in sample (some times expost)

Forecasting is out of sample (certainly ex ante)

Example if you have 2000-2017 gold price data .You can estimate an ARIMA model as using them. You predict 2017-2019 until today.And you can forecast tomorrrow or forever.