what is thye meaning of probablity?

Question

math

Answer 1

The quality or condition of being probable; likelihood.
A probable situation, condition, or event: Her election is a clear probability.

The likelihood that a given event will occur: little probability of rain tonight.
Statistics. A number expressing the likelihood that a specific event will occur, expressed as the ratio of the number of actual occurrences to the number of possible occurrences.

Answer 2

I will give you 3 different answers.

1.) The usual interpretation of probability in real life assumes that there is a certain experiment that can be repeated arbitrarily many times. In practice, if you count how many times a certain event occurs out of a large number of repeated experiments and compute in how many percent of all experiments it has happened, then this percentage gets closer and closer to some value as you perform more and more experiments (this phenomenon is called the empirical law of large numbers). The value this percentage approaches is the probability of the event (and it has to fall between 0 and 1, or, in other words, 0% and 100%).

For example, suppose that you toss a coin 10000 times and after the first 100 tosses, the percentage of heads is 60%, after 1000 tosses, it is 52%, and after 10000 tosses, it is 50.4%. It gets closer and closer to the value 50% (0.5), which is the probability of heads assuming that the coin is fair.

2.) Another interpretation of probability is the strength of the subjective belief of a person in the truth of a statement expressed on a scale from 0 to 1 (or from 0% to 100%).

For example, you might hear from the weather forecast that the probability of rain tomorrow is 75%. This is clearly not based on the first interpretation, because checking whether it will rain tomorrow is not an experiment that can be performed arbitrarily many times, so it's not possible to count in how many percent of the cases it rained tomorrow. Instead, it expresses that strength of the subjective belief of the experts who made the weather forecast in the statement that it will rain tomorrow is 75%: it's more likely that it will than it won't, but it's not certain.

3.) In mathematics, the concept of probability cannot be defined by either of the above interpretations, because mathematics has to work with very precisely defined concepts. This precision results in a high level of abstraction.

Probability theory (the field of mathematics studying probability) first defines the set of outcomes of an experiment. Then it defines the set of events, which consists of subsets of the set of outcomes. Finally, it assigns probabilities to the events.

(These three objects (the set of outcomes, the set of events and probability) have to possess some properties so that the whole model resembles the real life concept of probability.
a.) The set of outcomes can be any non-empty set.
b.) The set of events is a so-called sigma-algebra that consists of subsets of the set of outcomes.
c.) Probability is a function that assigns values in the interval [0,1] to the events such that it is non-negative, sigma-additive and the probability of the set of all outcomes is 1.)

For example, the set of all outcomes can be {1,2,3,4,5,6} if the experiment is throwing a dice and an event can be {1,3,5} (throwing an odd number). The probability of {1,3,5} is 0.5.

Interpretation 1.) is called the Frequentist interpretation of probability. Interpretation 2.) is called the Bayesian interpretation. These two result in two completely different schools of Statistics.
Approach 3.) is the mathematically precise definition of probability, which revolutionized probability theory and made it one of the most productive areas of research. This axiomatic approach was first published by Russian mathematician A.N.Kolmogorov in 1933 in his book "The Foundations of Probability Theory".

Answer 3

The probability of an event, noted p(event) is a number between 0 and 1.

If p=0, it means the event is impossible.
If p=1, the event is certain to happen.
If p=0.5, the event has a 50% chance of happening.

Examples.

p(tossing a coin once and landing on heads) = 0.5.
p(throwing a die once and getting a 6) = 1/6.
p(drawing a card at random from a deck and getting a spade) = 13/52 or 1/4.

Answer 4

The quality or condition of being probable; likelihood.
A probable situation, condition, or event: Her election is a clear probability.

The likelihood that a given event will occur: little probability of rain tonight.
Statistics. A number expressing the likelihood that a specific event will occur, expressed as the ratio of the number of actual occurrences to the number of possible occurrences.

1: a measure of how likely it is that some event will occur; "what is the probability of rain?"; "we have a good chance of winning" [syn: chance] 2: the quality of being probable [ant: improbability]

Answer 5

Probability is a ratio that is defined as "the number of positive outcomes over the number of possible outcomes"

Example: When rolling a fair six-sided die, the probability of rolling an even number is 3/6 which is 1/2
There are 3 even numbers on the die and 6 possible outcomes.

Hope this helps. :)

Answer 6

The meaning of probability is how likely it is that a certain (usually stated) situation will occur.

Example: How likely is it that when you toss two coins a certain number of times, they will both land face up.

hope this helps

Answer 7

In mathematics, it's the study of events that occur randomly or with degrees of uncertainty.

Answer 8

To see what is a chance of the particular thing happening...