Possible Outcomes when Two Dice are Rolled
A standard die has six sides numbering 1, 2, 3, 4, 5, and 6. If the die is fair, then each of these outcomes is equally likely event. Since there are six possible outcomes. The probability of getting any side of the die is 1/6. The probability of obtaining a 1 is 1/6, the probability of obtaining a 2 is 1/6, and so on.
The number of total possible outcomes is equal to the total numbers of the first die (6) multiplied by the total numbers of the second die (6), which is 36. So, the total possible outcomes when two dice are thrown together is 36.
The equally likely outcomes of rolling two dice are shown below:
(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)
Example: Suppose if we throw two die then what is the probability that the sum of two numbers is 10.
Favourable Outcome where the sum is 10 = (5, 5), (4, 6) and (6, 4)
Total Outcome = 36
Probability that the sum is 10 = 3/36 = 1/12
Rolling a Die
Rolling a Die is an important concept in Mathematics and its concepts are highly used in solving various problems of Probability. A die is a solid structure that is a cube with six faces and each of its faces is marked with a number from 1 to 6. And rolling a die there is equal probability that it lands on any of its faces, so each face has an equal probability of appearing. Now there are six faces so the probability of any one face is 1/6. The concept of Rolling a die is used in various games like Snake and Ladders, Ludo, Monopoly, various casino games, and others.
In this article we will learn about, What Rolling a Die means, the Probability of rolling a fair die, and others in detail.
Table of Content
- What Does Rolling a Die Mean?
- Probability of Rolling a Fair Dice
- Probability of a Number on Dice
- Possible Outcomes when Two Dice are Rolled
- Rolling a Die Examples
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