explain the difference of independent and dependent events.

Independent events are two or more events where the outcome of one event does not affect the outcome of another. In other words, the occurrence of one event has no influence on the probability of the other event occurring. A classic example of independent events is the toss of a coin. Each coin toss is independent of the others; the outcome of one coin toss (getting heads or tails) does not change the probability of getting heads or tails on the next toss.

Dependent events, on the other hand, are events where the outcome of one event does affect the outcome of another. In this case, the occurrence of one event influences the probability of the other event occurring. An example of dependent events is drawing cards from a deck without replacement. If you draw a card from a deck and do not put it back, the composition of the deck changes, therefore changing the probability of drawing a second card of a particular type. For instance, if you draw an ace from a deck of cards, the probability of drawing another ace on the next draw is reduced because there is one less ace in the deck.