Question

Explain, in your own words, what it means for two events to be considered independent. How are independent events different from dependent events? There are rules for independence that you might share; however, you need to also provide an explanation of the meaning of independent events.

Answer 1

Independent events are events that are not influenced by each other. In other words, the outcome of one event does not affect the outcome of the other event. For example, flipping a coin and rolling a dice are independent events because the outcome of one event (the coin flip) does not affect the outcome of the other event (the dice roll).

Dependent events, on the other hand, are events in which the outcome of one event does affect the outcome of the other event. For example, drawing a card from a deck and then drawing another card from the same deck are dependent events because the second draw is dependent on the first draw (since there is one less card in the deck after the first draw).

There are a few rules for determining if two events are independent or dependent:

If the outcome of one event does not affect the outcome of the other event, the events are independent.

If the probability of an event occurring changes based on the outcome of another event, the events are dependent.

If the events are not related to each other in any way, they are independent.

Overall, understanding whether events are independent or dependent is important in probability and statistics because it helps us to accurately predict the likelihood of certain outcomes occurring.