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# Independence versus Dependence

## Applications involving conditional probability and determining whether events are independent.

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Practice Independence versus Dependence

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What's Really Happening?

Did you know that from 350 BCE until 1668 CE it was widely accepted that maggots (fly larvae) were born from rotten meat? In other words, people incorrectly believed that the meat spawned the maggots!

#### Amazing But True

The 17th-century Italian physician Francesco Redi is regarded as the founder of modern experimental biology because of his contributions to the field medicine and because he successfully debunked the theory of spontaneous generation?the theory that living organisms could be born or spawned from non-living matter. This false idea was based on phenomena such as the seemingly magical appearance of maggots out of nowhere on rotten meat. At the time, people interpreted this observation as proof that the fly larvae were born directly from the spoiled meat. Until Redi discredited the theory, people did not yet have the scientific ability to recognize that flies had landed on the meat and laid eggs from which the maggots hatched.

When designing experiments, examining probabilities, and predicting events, it is critical to determine which events are dependent, which are independent, and which are overlapping. While maggots are born from the eggs of flies that land on rotten meat, the presence of spoiled meat is certainly not the only factor determining when, where, and how maggots hatch?maggots are not the result of rotten meat spontaneously turning into maggots! However, it required years of study, careful experimentation, and examination of varying events for scientists to determine that maggots were the result of flies and not the meat itself.

#### Explore More

You decide to press the snooze button on your alarm clock one morning, and wake up with only 15 minutes to catch the bus! You quickly brush your teeth, get dressed, grab your backpack, and race out the door to the bus stop. Thankfully, the bus is 3 minutes late, and you catch it just before it pulls away. Are the events of your hitting the snooze button and the bus?s arriving late dependent or independent events?

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