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QExplain in your own words, using the definition of probability why: a) the probability of an event that cannot occur is 0; b) the probability of an event that must occur is 1

Explain in your own words, using the definition of probability why: a) the probability of an event that cannot occur is 0; b) the probability of an event that must occur is 1.


i posted this in class:P(event) = (# of ways to succeed)/(# of ways to succeed + # of ways to fail)


a)the probability of an event that cannot occur is 0

If it cannot occur the # of ways to succeed is zero

Then P(event) = 0/(# of ways to fail) = 0


b) the probability of an event that must occur is 1.

If it must occur the # of ways to fail is zero

Then P(event) = (# of ways to succeed)/(# of ways to succeed) = 1


but my teacher wants something more detail as an explanation.. Can you please help.. I do not know what she wants from me...

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#1fubuAnswered at 2013-03-15 18:19:01
Number of Elements in Event Space P(Some Event) = ------------------------------------- Number of Elements in Sample Space
#2CoreAnswered at 2013-03-15 18:19:26
Here's one way you can think of probability: Probability is simply a fraction composed of the number of elements in the event space over the number of events in the sample space. Recall that the sample space is the set of ALL possible outcomes and the event space is the set of desirable outcomes. In other words, <pre> Number of Elements in Event Space P(Some Event) = ------------------------------------- Number of Elements in Sample Space </pre> note: the notation P(Some Event) is shorthand for saying "The probability of Some Event" Now if there are NO elements in the event space, ie if the desirable event does NOT occur (not even once), then the numerator is equal to zero. This points to the entire probability equaling zero (which means that there's a 0% chance of it happening). Or, if on the other hand that the number of elements in the event space equals the number of elements in the sample space, then no matter which element you choose, you will ALWAYS get what you desired. This means that the fraction will then equal 1 (which points to a 100% probability). Note: you will rarely see probabilities of 0% and 100% simply because there are very few things that are certain. If life was certain, then why have probability at all?
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Explain in your own words, using the definition of probability why: a) the probability of an event that cannot occur is 0; b) the probability of an event that must occur is 1

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