# Wikipedia:Reference desk/Archives/Mathematics/2008 September 19

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# September 19

## probability

what is the probability of 1.0 means? and between probability of 1.0 and o.4 which the best to present the survival without parasitemia —Preceding unsigned comment added by 41.221.34.123 (talk) 07:53, 19 September 2008 (UTC)

A probability of 1 means that it is certain (100% likely) to occur. A probability of 0 means it is certain to never occur, 0.5 means the event will happen half (50%) of the time. A probability cannot be less than 0 nor can it be greater than 1. -- SGBailey (talk) 07:58, 19 September 2008 (UTC)
This is wrong. If an event has probability 1, it does not mean that it is certain. For example, consider the event of randomly picking a number in [0,1]. The probability that you pick a number other than 0 is 1 but it is not certain that you will not pick a 0.

See Almost surely.

Topology Expert (talk) 05:44, 20 September 2020 (UTC)

Please clarify your second question. Are you asking whether 1 or 0.4 is a more reasonable measure of a survival rate without parasitemia? Note that survival rates are usually associated with a certain length of time. Zain Ebrahim (talk) 14:15, 19 September 2008 (UTC)

Though maybe it should be noted, from a mathematical and not at all practical stand point, that probability 1 is not quite certain and probability 0 is not quite "certainly not". Thenub314 (talk) 14:57, 19 September 2008 (UTC)

Eh? From a mathematical point of view, 1 is certain and 0 is certainly not. From a colloquial point of view then anything goes. Use "Acme's gadget for 110% success" is gibberish mathematically. -- SGBailey (talk) 15:16, 19 September 2008 (UTC)
1 is not certain; see my previous comment.

Topology Expert (talk) 05:47, 20 September 2008 (UTC)

What Thenub314 means is that any set with measure zero has probability zero, not just the empty set. Pick a random real number between 0 and 1. The probability of your picking that number was 0, yet you picked it. -- BenRG (talk) 16:28, 19 September 2008 (UTC)
We have an article: almost surely. Algebraist 16:31, 19 September 2008 (UTC)
Note that there is a subtle difference here between the theory and practice in that we have no way to pick a random real number between 0 and 1. So when you pick a random real number, it actually has some nonzero probably. Even with a true random number generator, there is only a finite list of expressible numbers.
To my knowledge, everything in practice is a finite process, and so there is no practical distinction between almost surely, and certain: and the OP probably doesn’t know any measure theory. GromXXVII (talk) 13:30, 21 September 2008 (UTC)