Question

The probability of the empty set
\[P(\emptyset )=\]

Answer 1

What does this mean

Answer 2

0

Answer 3

0

Answer 4

\[P \left( \emptyset \right) = 0\]

Answer 5

ok ,
but i dont undertand

Answer 6

I was guessing :P

Answer 7

well, yeah The probability of the empty set is zero ,

but what does this mean?

Answer 8

how can it be shown?

Answer 9

empty set is an impossible event

Answer 10

P(S) = 1

\[S \cup \emptyset = S\]

\[S \cap \emptyset = \]
so, \[S and \emptyset \] are mutually exclusive

\[P \left( S \right) = P \left( S \cup \emptyset \right) = P \left( S \right) + P (\emptyset) \]
\[P \left( S \right) = 1 ; \]

\[1 = 1 + P (\emptyset) \]
\[ P (\emptyset) = 0 \]

Answer 11

\[S \cap \emptyset =\emptyset \]

Answer 12

you have answered my question well,

\[S∪∅=S\iff P(\emptyset)=0\]

Answer 13

to determine the probability you must have an event ,

is the empty set a lack of events

Answer 14

@UnkleRhaukus you are judging math by your preconditioned intuition.
In fact probaility with sets has a generally unified (and mostly used) set of Kolmogorov foundation. Today this is the foundation used everywhere except in some esoteric and very rare circumstances.
http://en.wikipedia.org/wiki/Probability_axioms

Answer 15

i am questioning not judging ,

Answer 16

Well empty set can be intuited differently - such event taht NO outcomes can make it truly occur. That is, the EventOccurenceTruthFunction(outcome) = False for all possible outcomes

Answer 17

empty set = false ?

Answer 18

=impossible = no solutions ?

Answer 19

Look up what is Truth Function. It characterizes "happened or did not happen"

Answer 20

For example TruthOdd(outcome 4) = False
TruthOdd(outcome 3) = True

Answer 21

ok thanks

Answer 22

@UnkleRhaukus
yes.., it's what I mean \[S \cap \emptyset = \emptyset\]

Answer 23

what do you mean by
S and ∅
are mutually exclusive,

Answer 24

mutually exclusive events are events that cannot occur at the same time,