This sample space is infinite because there’s an infinite number of real numbers in the interval. The simplest example of an infinite sample space I can think of is that of randomly drawing a number between 0 and 1. An infinite sample space has an infinite number of possible outcomes. A finite sample space is one which has a finite number of possible outcomes.
![non zero over zero limits non zero over zero limits](https://media.cheggcdn.com/study/999/999ea0c7-b9c6-4660-8abc-256763421958/image.png)
On the other hand, in infinite sample spaces, possible zero probability outcomes are abundant.Ī sample space is simply the set of all possible outcomes of some randomness or uncertainty. So, how can an outcome be possible, yet have a probability of zero? You can’t come up with any examples while staying in the realm of finite sample spaces. Possible outcomes with zero probabilities What is not true is that zero probability outcomes are necessarily impossible. It’s still true that impossible outcomes have a probability of zero. The apparent contradiction is resolved by noticing that I approached the question from two different directions.
![non zero over zero limits non zero over zero limits](https://images.slideplayer.com/25/7772671/slides/slide_3.jpg)
But just now I implied that impossible outcomes always have a probability of 0. Have you noticed a contradiction so far? In the beginning I said that a probability of zero doesn’t imply an outcome is impossible to occur. The zero in the numerator comes from the fact that exactly 0 of the six possible outcomes are 8. You can still get this probability by dividing by the total number of possible outcomes: For example, you can’t roll an 8 with a 6-sided die. If an outcome isn’t in the set of possible outcomes, by definition it can’t occur. The logic here is simply to divide the number of outcomes that satisfy an event by the total number of possible outcomes. The probability of drawing the jack of diamonds from a standard 52-card deck is 1/52. Therefore, the probability of heads is 1 out of 2, or 1/2.īy the same logic, the probability of rolling a 4 with a 6-sided die is 1/6. You probably came up with this answer by a thought process like: You’re flipping a coin and considering the probability of getting heads. Let’s start with some simple probability examples.
![non zero over zero limits non zero over zero limits](https://www.researchgate.net/profile/Helen-Byrne-5/publication/43226392/figure/fig1/AS:271381359230978@1441713766526/Typical-phase-planes-A-Typical-phase-plane-with-non-zero-nullclines-for-case-a.png)