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What are the possible outcomes when two dice are rolled?

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  • Last Updated : 30 Dec, 2021

Probability is a part of mathematics that deals with the possibility of happening of events. It is to forecast that what are the possible chances that the events will occur or the event will not occur. The probability as a number lies between 0 and 1 only and can also be written in the form of a percentage or fraction. The probability of likely event A is often written as P(A). Here P shows the possibility and A shows the happening of an event. Similarly, the probability of any event is often written as P(). When the end outcome of an event is not confirmed we use the probabilities of certain outcomes—how likely they occur or what are the chances of their occurring.

To understand probability more accurately we take an example as rolling a dice:

The possible outcomes are — 1, 2, 3, 4, 5, and 6.

The probability of getting any of the outcomes is 1/6. As the possibility of happening of an event is an equally likely event so there are same chances of getting any number in this case it is either 1/6 or 50/3%.

Formula of Probability

Probability of an event, P(A) = (Number of ways it can occur) ⁄ (Total number of outcomes)

Types of Events

  • Equally Likely Events: After rolling dice, the probability of getting any of the likely events 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: There is a possibility of only two outcomes which is an event will occur or not. Like a person will play or not play, buying a laptop or not buying a laptop, etc. are examples of complementary events.

What are the possible outcomes when two dice are rolled?

Answer:

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)

Similar Problems

Question 1: What are the total possible outcomes when five dice are thrown together?

Solution:

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)multiplied by the total number of the third die(6), and so on, which is 7776. So, the total possible outcomes when three dies are thrown together is 7776.  

Question 2: What are the total possible outcomes when six dice are thrown together?

Solution:

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)multiplied by the total number of the third die(6)multiplied by the total number of the fourth die(6), and so on… which is 46656.  

So, the total possible outcomes when four dies are thrown together is 46656.

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