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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 π 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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