The Binomial - This proportion, , remains constant...

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The Binomial A discrete variable that can result in only one of two outcomes is called  binomial . For example, a  coin flip is a binomial variable, but drawing a card from a standard deck of 52 is not. Whether a drug  is successful or unsuccessful in producing results is a binomial variable, as is whether a machine  produces perfect or imperfect widgets.  Binomial experiments Binomial experiments require the following elements:  The experiment consists of a number of identical events (  n ).  Each event has only one of two mutually exclusive outcomes. (These outcomes are  called successes and failures.) The probability of a success outcome is equal to some percentage, which is  identified as a  proportion,   .  π
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Unformatted text preview: This proportion, , remains constant throughout all events and is defined as the ratio of number of successes to number of trials. The events are independent. Given all the above, the binomial formula can be applied ( x = number of favorable outcomes; n = number of events): Example 1 A coin is flipped ten times. What is the probability of getting exactly five heads? Using the binomial formula, where n (the number of events) is given as 10; x (the number of favorable outcomes) is given as 5; and the probability of landing a head in one flip is 0.5: So, the probability of getting exactly five heads in ten flips is 0.246, or approximately 25 percent....
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The Binomial - This proportion, , remains constant...

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