Question
Which type of compound event is generally associated with multiplication? Which is generally associated with addition?
Ask by Weber West. in the United States
Mar 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Multiplication is used for independent events, while addition is used for mutually exclusive events in probability.
Solution
In probability, compound events can be categorized based on how they are combined:
-
Multiplication: This is generally associated with independent events. When you want to find the probability of two independent events both occurring, you multiply their probabilities. For example, if event A has a probability of
and event B has a probability of , the probability of both A and B occurring is given by: -
Addition: This is generally associated with mutually exclusive events. When you want to find the probability of either event A or event B occurring (and they cannot happen at the same time), you add their probabilities. For example, if event A has a probability of
and event B has a probability of , the probability of either A or B occurring is given by:
In summary:
- Multiplication: Independent events
- Addition: Mutually exclusive events
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Simplify this solution Beyond the Answer
When considering compound events, independent events are generally associated with multiplication. This is because the probability of two independent events occurring together is found by multiplying their individual probabilities. For instance, if you flip a coin and roll a die, the chance of getting heads and a three is the product of their individual probabilities.
On the other hand, mutually exclusive events are typically associated with addition. When you want to determine the probability of either one event or another occurring, such as rolling a 2 or a 5 on a die, you simply add their probabilities together. This reflects the idea that if one event happens, the other cannot happen at the same time—like choosing one flavor of ice cream over another!
