Statistics & Probability

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Classifying Multiples with Venn Diagram.pdf

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Monty Hall Problem (Interactive with explanation)

When you here the word probability, what do you think of? Maybe the word chance comes to mind. Mathematicians use the term events to describe things that happen. When discussing the probability of an “event” if something will always happen, it has a probability of one. If something has no chance of happening, the probability is zero.

Can you think of examples of events with zero or one probability? An event with a probability of zero could be a person lifting a house off its foundation by him/herself. An event with a probability of one may be rolling either a 1, 2, 3, 4, 5, or 6 on a number cube. Most events however, will have a probability between zero and one. The more likely it is to occur the closer it will be to one and the less likely it is to occur, the closer it is to zero.

Think of flipping a coin. What are the chances of a head? a tail? We would say that the coin being flipped either as a head or tail has an equal chance (or 50 percent chance) of occurring.

Events can be describes as either independent or dependent events. An independent event is an event that is not affected by any other event whether or not the event(s) happen before or after. A dependent event is affected by the outcome of events that occurred before.

A common misconception that people have is confusing independent and dependent events. For example let’s say that we flipped a coin and seven times in a row it came up heads. What is the probability that the eighth flip will produce a “head” flip? Many people say the probability is very low, or close to zero, but in reality it is still a 50 percent chance of landing “heads.” The eighth flip has no bearing (or are not dependent upon) the previous seven. Each time you flip a coin, it is considered an independent event.

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Taken by Olivander