Probability of null set
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We know that the probability of an impossible event is 0. But is the inverse true? That is, if probability of an event is 0, does it necessarily imply the fact that the event is impossible event? If not, give an example please to understand this concept.
Thanks in advance.
probability
asked Nov 18 at 14:59
user587389
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up vote
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down vote
favorite
We know that the probability of an impossible event is 0. But is the inverse true? That is, if probability of an event is 0, does it necessarily imply the fact that the event is impossible event? If not, give an example please to understand this concept.
Thanks in advance.
probability
asked Nov 18 at 14:59
user587389
326
2
Suppose you choose a real number uniformly at random from the interval $[0,1]$. The probability that it is exactly $frac 12$ is $0$, but it is not impossible. Same sort of observation holds for any continuous distribution.
– lulu
Nov 18 at 15:00
Only from a practicality standpoint. Events with probability zero are those for which a procedure can be done over and over forever and is never expected to occur.
– David Peterson
Nov 18 at 15:03
No. See If $ P(A) = 0 $ is $ A $ a null event?.
– Dave L. Renfro
Nov 18 at 15:19
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
We know that the probability of an impossible event is 0. But is the inverse true? That is, if probability of an event is 0, does it necessarily imply the fact that the event is impossible event? If not, give an example please to understand this concept.
Thanks in advance.
probability
asked Nov 18 at 14:59
user587389
326
We know that the probability of an impossible event is 0. But is the inverse true? That is, if probability of an event is 0, does it necessarily imply the fact that the event is impossible event? If not, give an example please to understand this concept.
Thanks in advance.
probability
probability
asked Nov 18 at 14:59
user587389
326
asked Nov 18 at 14:59
user587389
326
asked Nov 18 at 14:59
user587389
326
asked Nov 18 at 14:59
user587389
326
asked Nov 18 at 14:59
user587389
326
326
2
Suppose you choose a real number uniformly at random from the interval $[0,1]$. The probability that it is exactly $frac 12$ is $0$, but it is not impossible. Same sort of observation holds for any continuous distribution.
– lulu
Nov 18 at 15:00
Only from a practicality standpoint. Events with probability zero are those for which a procedure can be done over and over forever and is never expected to occur.
– David Peterson
Nov 18 at 15:03
No. See If $ P(A) = 0 $ is $ A $ a null event?.
– Dave L. Renfro
Nov 18 at 15:19
add a comment |
2
Suppose you choose a real number uniformly at random from the interval $[0,1]$. The probability that it is exactly $frac 12$ is $0$, but it is not impossible. Same sort of observation holds for any continuous distribution.
– lulu
Nov 18 at 15:00
Only from a practicality standpoint. Events with probability zero are those for which a procedure can be done over and over forever and is never expected to occur.
– David Peterson
Nov 18 at 15:03
No. See If $ P(A) = 0 $ is $ A $ a null event?.
– Dave L. Renfro
Nov 18 at 15:19
2
2
Suppose you choose a real number uniformly at random from the interval $[0,1]$. The probability that it is exactly $frac 12$ is $0$, but it is not impossible. Same sort of observation holds for any continuous distribution.
– lulu
Nov 18 at 15:00
Suppose you choose a real number uniformly at random from the interval $[0,1]$. The probability that it is exactly $frac 12$ is $0$, but it is not impossible. Same sort of observation holds for any continuous distribution.
– lulu
Nov 18 at 15:00
Only from a practicality standpoint. Events with probability zero are those for which a procedure can be done over and over forever and is never expected to occur.
– David Peterson
Nov 18 at 15:03
Only from a practicality standpoint. Events with probability zero are those for which a procedure can be done over and over forever and is never expected to occur.
– David Peterson
Nov 18 at 15:03
No. See If $ P(A) = 0 $ is $ A $ a null event?.
– Dave L. Renfro
Nov 18 at 15:19
No. See If $ P(A) = 0 $ is $ A $ a null event?.
– Dave L. Renfro
Nov 18 at 15:19
add a comment |
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Suppose you choose a real number uniformly at random from the interval $[0,1]$. The probability that it is exactly $frac 12$ is $0$, but it is not impossible. Same sort of observation holds for any continuous distribution.
– lulu
Nov 18 at 15:00
Only from a practicality standpoint. Events with probability zero are those for which a procedure can be done over and over forever and is never expected to occur.
– David Peterson
Nov 18 at 15:03
No. See If $ P(A) = 0 $ is $ A $ a null event?.
– Dave L. Renfro
Nov 18 at 15:19