Probability is a part of math which deals with the possibility of happening random events. It is to predict how likely the events will occur or the event will not occur. The probability of happening an event is between 0 and 1 only and can also be written in the form of a percentage or fraction. The probability of event B is often written as P(B). Here P indicates the possibility and B indicate the happening of an event. Similarly, the probability of any event is often written as P(). When the end result of an event is not confirmed we use the probabilities of certain consequences—how likely they occur or what are the chances of their occurring. Show
The unpredictability of ‘probably’ etc., can be calculated numerically by means of ‘probability’ in many cases. Though probability started with a bet, it has been used carefully in the fields of Physical Sciences, Commerce, Biological Sciences, Medical Sciences, Weather Forecasting, etc. To understanding probability we take an example as rolling a dice: There are six possible outcomes— 1, 2, 3, 4, 5, and 6. The probability of getting any of the numbers is 1/6. As the event is an equally likely event so there is same possibility of getting any number in this case it is either 1/6 or 50/3%. Formula of Probability Probability of an event = {Number of ways it can occur} ⁄ {Total number of outcomes}
Types of EventsEqually Likely Events: Rolling a dice the probability of getting any of the numbers is 1/6. As the event is an equally likely event so there is same possibility of getting any number in this case it is either 1/6 in fair dice rolling. Complementary Events: Possibility of only two outcomes which is an event will occur or not. Like a person will eat or not eat the pizza, buying a bullet or not buying a bullet, etc. are examples of complementary events. Solution: The three dice are fair, that are not biased in any manner whatsoever. The dice has 6 faces with a number between 1 and 6 inclusive, on each face with no matching numbers and no vacant faces. The three dice are rolled fairly without any cheating. Each of the dice rolls is an Independent Event, that is the outcome from anyone dice roll has no impact whatsoever on the outcome of any other dice roll.
Similar QuestionsQuestion 1: A coin is tossed 1000 times with the following frequencies: Head: 455, Tail: 545 Compute the probability for each event. Solution:
Question 2: What is the probability of rolling three dice and none match? Solution:
 Contents: Watch the video for three examples: Probability: Dice Rolling Examples Watch this video on YouTube. Can’t see the video? Click here. Need help with a homework question? Check out our tutoring page! Dice roll probability: 6 Sided Dice ExampleIt’s very common to find questions about dice rolling in probability and statistics. You might be asked the probability of rolling a variety of results for a 6 Sided Dice: five and a seven, a double twelve, or a double-six. While you *could* technically use a formula or two (like a combinations formula), you really have to understand each number that goes into the formula; and that’s not always simple. By far the easiest (visual) way to solve these types of problems (ones that involve finding the probability of rolling a certain combination or set of numbers) is by writing out a sample space. Dice Roll Probability for 6 Sided Dice: Sample SpacesA sample space is just the set of all possible results. In simple terms, you have to figure out every possibility for what might happen. With dice rolling, your sample space is going to be every possible dice roll. Example question: What is the probability of rolling a 4 or 7 for two 6 sided dice? In order to know what the odds are of rolling a 4 or a 7 from a set of two dice, you first need to find out all the possible combinations. You could roll a double one [1][1], or a one and a two [1][2]. In fact, there are 36 possible combinations. Dice Rolling Probability: StepsStep 1: Write out your sample space (i.e. all of the possible results). For two dice, the 36 different possibilities are: [1][1], [1][2], [1][3], [1][4], [1][5], [1][6], [2][1], [2][2], [2][3], [2][4], [2][5], [2][6], [3][1], [3][2], [3][3], [3][4], [3][5], [3][6], [4][1], [4][2], [4][3], [4][4], [4][5], [4][6], [5][1], [5][2], [5][3], [5][4], [5][5], [5][6], [6][1], [6][2], [6][3], [6][4], [6][5], [6][6]. Step 2: Look at your sample space and find how many add up to 4 or 7 (because we’re looking for the probability of rolling one of those numbers). The rolls that add up to 4 or 7 are in bold: [1][1], [1][2], [1][3], [1][4], [1][5], [1][6], There are 9 possible combinations. Step 3: Take the answer from step 2, and divide it by the size of your total sample space from step 1. What I mean by the “size of your sample space” is just all of the possible combinations you listed. In this case, Step 1 had 36 possibilities, so: 9 / 36 = .25 You’re done! Two (6-sided) dice roll probability tableThe following table shows the probabilities for rolling a certain number with a two-dice roll. If you want the probabilities of rolling a set of numbers (e.g. a 4 and 7, or 5 and 6), add the probabilities from the table together. For example, if you wanted to know the probability of rolling a 4, or a 7:
Probability of rolling a certain number or less for two 6-sided dice.
Dice Roll Probability TablesContents: Probability of a certain number with a Single Die.
Probability of rolling a certain number or less with one die.
Probability of rolling less than certain number with one die.
Probability of rolling a certain number or more.
Probability of rolling more than a certain number (e.g. roll more than a 5).
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Visit out our statistics YouTube channel for hundreds of probability and statistics help videos! ReferencesDodge, Y. (2008). The Concise Encyclopedia of Statistics. Springer.
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When 3 dice are rolled what is the probability of getting a sum of 6?
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