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What are the total possible outcomes when two dice are thrown simultaneously?

  • Last Updated : 10 Nov, 2021

Another word for probability is a possibility. It is a math of chance, that deals with the happening of a random event. The value is indicated from zero to one. In math, Probability has been introduced to predict how likely events are to occur. The meaning of probability is basically the scope to which something is to be expected to happen.

  • Frequency interpretation: Probabilities are recognized as mathematically suitable estimation to long run respective frequencies.
  • Subjective interpretation: A probability statement indicates the belief of some person regarding how certain an event is likely to occur.

To understand probability more accurately, 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 possible outcomes is 1/6. As the possibility of happening any of an event is the same so there are equal chances of getting any likely number in this case it is either 1/6 or 50/3%.

Formula of Probability

Since probability is the possibility of an outcome. Therefore, it is basically a ratio. In proper words, it can be said that probability is the ratio of the expected outcomes to the total number of outcomes.

Probability of an event = {Number of ways it can occur} ⁄ {Total number of outcomes}

P(A) = {Number of ways A occurs} ⁄ {Total number of outcomes}

Lets take a look at the two important types of events in probability. They are equally likely events and complementary 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 some possibility of obtaining any number in this case it is either 1/6 in fair dice rolling.
  • Complementary Events: There is a probability or possibility of only two outcomes which is an event will occur or not. Like a person will eat or not eat, buying a car or not buying a car, etc. are examples of complementary events.

What are the total possible outcomes when two dice are thrown simultaneously?

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), 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 in the table below:

 123456
1(1, 1)(1, 2)(1, 3)(1, 4)(1, 5)(1, 6)
2(2, 1)(2, 2)(2, 3)(2, 4)(2, 5)(2, 6)
3(3, 1)(3, 2)(3, 3)(3, 4)(3, 5)(3, 6)
4(4, 1)(4, 2)(4, 3)(4, 4)(4, 5)(4, 6)
5(5, 1)(5, 2)(5, 3)(5, 4)(5, 5)(5, 6)
6(6, 1)(6, 2)(6, 3)(6, 4)(6, 5)(6, 6)

Similar Problems

Question 1: What are the total possible outcomes when three 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), which is 216. So, the total possible outcomes when three dies are thrown together is 216. 

Question 2: What are the total possible outcomes when four 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), which is 1296. 

So, the total possible outcomes when four dies are thrown together is 1296.

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