Question

Explain the difference between independent and dependent events.

Answer 1

Independent events in probability do not affect each other's outcomes, with an example being two rolls of a fair die, while dependent events do affect each other, such as drawing cards from a deck without replacement. The probability rules for independent events are specific and include formulas such as P(A AND B) = P(A)P(B).

Step-by-step explanation:

In the context of probability, independent events are scenarios where the occurrence of one event does not affect the probability of the other event occurring. On the other hand, dependent events are those where the occurrence of one event has an effect on the likelihood of the other event taking place.

For example, two rolls of a fair die are independent because the result of the first roll does not impact the result of the second roll. This is reflected in probability calculations where the probability of both independent events occurring is equal to the product of their individual probabilities: P(A AND B) = P(A)P(B). Conversely, if you draw two cards from a deck without replacement, these are dependent events as the outcome of the first draw changes the probability of the second draw because the deck's composition has been altered.

To show that events A and B are independent, the following must be true: P(B|A) = P(B), indicating that the probability of B given that A has occurred is the same as the probability of B on its own. When sampling is done with replacement, events are typically considered independent since the first pick does not alter the likelihood of subsequent picks.

Answer 2

I’m an independent event things are changing and in a dependent event things are normally being measured. Other means are you are independent by wanting to go around and only depending on yourself. For example you’re an independent learner (you learn better alone and not in a group setting or partner work). Dependent is when you are always relying on others and always yearning for help. For example you can’t take tests or learn by yourself you always need help from other people.