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probability

# probability - Probability Probability what is the chance...

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Probability Probability : what is the chance that a given event will occur? For us, what is the chance that a child, or a family of children, will have a given phenotype? Probability is expressed in numbers between 0 and 1. Probability = 0 means the event never happens; probability = 1 means it always happens. The total probability of all possible event always sums to 1.

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Definition of Probability The probability of an event equals the number of times it happens divided by the number of opportunities. These numbers can be determined by experiment or by knowledge of the system. For instance, rolling a die (singular of dice). The chance of rolling a 2 is 1/6, because there is a 2 on one face and a total of 6 faces. So, assuming the die is balanced, a 2 will come up 1 time in 6. It is also possible to determine probability by experiment: if the die were unbalanced (loaded = cheating), you could roll it hundreds or thousands of times to get the actual probability of getting a 2. For a fair die, the experimentally determined number should be quite close to 1/6, especially with many rolls.
The AND Rule of Probability The probability of 2 independent events both happening is the product of their individual probabilities. Called the AND rule because “this event happens AND that event happens”. For example, what is the probability of rolling a 2 on one die and a 2 on a second die? For each event, the probability is 1/6, so the probability of both happening is 1/6 x 1/6 = 1/36. Note that the events have to be independent : they can’t affect each other’s probability of occurring. An example of non-independence: you have a hat with a red ball and a green ball in it. The probability of drawing out the red ball is 1/2, same as the chance of drawing a green ball. However, once you draw the red ball out, the chance of getting another red ball is 0 and the chance of a green ball is 1.

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The OR Rule of Probability The probability that either one of 2 different events will occur is the sum of their separate probabilities. For example, the chance of rolling either a 2 or a 3 on a die is 1/6 + 1/6 = 1/3.
NOT Rule The chance of an event not happening is 1 minus the chance of it happening. For example, the chance of not getting a 2

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probability - Probability Probability what is the chance...

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