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Chapter 12: Problem 1

WRITING Explain the difference between dependent events and independent events, and give an example of each.

Short Answer

Expert verified
Independent events are those where the outcome of one event does not impact the probability of another, like tossing a coin and rolling a die. Dependent events are where the outcome of one event does influence the probability of the other, like drawing cards from a deck without replacement.

Step by step solution

01

Explain Independent Events

In probability theory, independent events refer to events that do not affect each other's outcomes. In other words, the occurrence of one event does not influence the likelihood of the other event happening. An example could be tossing a coin and rolling a die. The outcome of the coin toss (whether it's heads or tails) does not impact the result of the die roll (any number from 1 to 6). They are two separate events, and the outcome of one doesn't change the probability of the outcome of the other.
02

Explain Dependent Events

On the other hand, dependent events are events where the outcome of one event does affect the outcome of the other. In essence, the probability of the second event is influenced by the outcome of the first event. An illustration is picking cards from a deck without replacement. Assuming the first card picked is not replaced back into the deck, this affects the probability of the cards that can be drawn second. If the first card is a diamond, there are now fewer diamonds left in the deck, influencing the probability of drawing a diamond as the second card.
03

Summarize the Difference

To summarize, the principal difference between dependent and independent events lies in whether or not the outcome of one event influences the outcome of another. Independent events do not impact each other, while dependent events do. The illustrations of tossing a coin and rolling a die, as well as drawing cards from a deck without replacement, demonstrate these differences.

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