How do independent events differ from dependent events?

How do independent events differ from dependent events?

• A. Independent: one outcome has nothing to do with another; Dependent: one outcome depends on the occurrence of another
• B. Independent: outcomes always occur together; Dependent: outcomes never occur together
• C. Independent: order of events matters; Dependent: order does not matter
• D. Independent: probabilities must sum to 1; Dependent: probabilities never sum to 1

Answer: (A)

Two events are independent when the result of one does not change the probability of the other. For example, flipping a fair coin twice: the second flip has the same 50% chance of heads regardless of what happened on the first flip. When events are dependent, the outcome of the first event affects the probability of the second. A common example is drawing cards from a deck without replacement: after you draw one card, the composition of the remaining deck changes, so the chance of the next card having a given property changes as well. So, independent means one outcome has no influence on the other; dependent means the first outcome changes the likelihood of the second. The other descriptions don’t fit: independent events don’t have to happen together, they just don’t affect each other; order of events is about sequence, not dependence; and probabilities summing to 1 is a general rule for outcomes of a single experiment, not a feature that distinguishes independent from dependent events.

Two events are independent when the result of one does not change the probability of the other. For example, flipping a fair coin twice: the second flip has the same 50% chance of heads regardless of what happened on the first flip.

When events are dependent, the outcome of the first event affects the probability of the second. A common example is drawing cards from a deck without replacement: after you draw one card, the composition of the remaining deck changes, so the chance of the next card having a given property changes as well.

So, independent means one outcome has no influence on the other; dependent means the first outcome changes the likelihood of the second.

The other descriptions don’t fit: independent events don’t have to happen together, they just don’t affect each other; order of events is about sequence, not dependence; and probabilities summing to 1 is a general rule for outcomes of a single experiment, not a feature that distinguishes independent from dependent events.