Conquer ALEKS 2026 – Max Your Knowledge Spaces with Ease!

An independent event in probability refers to occurrences where the outcome of one event does not influence the outcome of another event. The example of rolling a die and flipping a coin illustrates this concept perfectly. When you roll a die, the result can be any of the six sides (1 through 6) and is unaffected by the result of flipping a coin, which can land on either heads or tails. Each event has its own separate probabilities, and knowing the outcome of one does not provide any information about the outcome of the other.

In contrast, drawing marbles from a bag without replacement means that the outcome of the first draw affects the probabilities of subsequent draws, as the number of marbles changes. Likewise, selecting a card from a deck introduces dependence, since the card is removed, changing the total number of cards in the deck for any additional draws. Selecting a student from a class also involves dependency on factors that can change the composition of choices, whereas rolling a die and flipping a coin remain independent events.