Flipping a fair coin where “heads” is considered a success ($𝑝=0.5$) and “tails” a failure ($1-𝑝=0.5$).

Rolling a die and checking if the outcome is a 6 (success) or not (failure). If the die is fair, the probability of success is $𝑝=\frac{1}{6}$ and the probability of failure is $1-𝑝=\frac{5}{6}$.

Checking whether a shipment arrives on time (success) or is delayed (failure). If historical data shows that a shipment has a 90% chance of arriving on time, the probability of success ($𝑝$) is 0.9, and the probability of failure ($1-𝑝$) is 0.1.