Is this an equivalent formula for P(A or B or C) ?

In summary, "P(A or B or C)" represents the probability of at least one of the events A, B, or C occurring and can be used to calculate the likelihood of multiple events happening in one trial. Two formulas are considered equivalent if they have the same values for all possible inputs, and this formula can be applied to any number of events by following the laws of probability.
  • #1
opticaltempest
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I was trying to derive a formula to find [tex]P(A \cup B \cup C)[/tex].

I came up with the following:

http://img249.imageshack.us/img249/2154/probabilitymp7.jpg

Is that correct?
 
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  • #2
Yes it's correct
 
  • #3

FAQ: Is this an equivalent formula for P(A or B or C) ?

What does "P(A or B or C)" mean in this formula?

"P(A or B or C)" represents the probability of at least one of the events A, B, or C occurring. This means that the formula is asking for the likelihood that at least one of the events will happen.

Can you provide an example of this formula in action?

Sure, let's say we have three events: flipping a coin and getting heads (A), rolling a six-sided die and getting a 3 (B), and drawing a red card from a deck of cards (C). The formula "P(A or B or C)" would represent the probability of getting heads, rolling a 3, or drawing a red card in one trial.

What does it mean for two formulas to be equivalent?

Two formulas are considered equivalent if they have the same values for all possible inputs. In the context of probability, this means that both formulas would give the same result for the probability of an event occurring.

How can I determine if a formula is an equivalent for "P(A or B or C)"?

To determine if a formula is an equivalent for "P(A or B or C)", you can check if the formula follows the laws of probability, such as the addition rule for mutually exclusive events and the inclusion-exclusion principle for non-mutually exclusive events.

Can this formula be applied to more than three events?

Yes, this formula can be applied to any number of events. For example, "P(A or B or C or D)" would represent the probability of at least one of the events A, B, C, or D occurring. The same principles and laws of probability would apply for any number of events in this formula.

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