For any group of unrelated events, the probability they happen together is the product of their probabilities.

If the chance of some scenario happening in p, then the probability it happens n times independently is ${p}^{n}$

Example if you toss a coin, the probability to guess the winning side on the first time is 1/2; two times on the row is 1/4; three times 1/8; 4 times 1/16

Applying Probability Rules

If the events have certain dependency and can't happen in the same time, you sum the probabilities

e.g., flight to be canceled and to be overbooked; these two events are distinct, you can't have a flight that is canceled and overbooked

If the events are independent and can happen in the same time, you multiply the probabilities

e.g., one flight can be delayed by wind, second flight can be delayed by traffic; any of these events are independent, so the chance to arrive in time by taking both flights, you need to use the product rule

Events

Independent events: The occurrence of one event does not affect the probability of the other event. For example, when flipping a coin, getting “heads” does not change the likelihood of getting “heads” on the next coin flip.

Dependent events: The occurrence of one event does affect the probability of the other event. For example, if you draw a King from a deck of cards and do not replace it, it causes the probability of drawing another King to decrease.