# In a single throw of two dice, what is the probability of getting a sum of 9?

By BYJU'S Exam Prep

Updated on: September 25th, 2023

**In a single throw of two dice, the probability of getting a sum of 9 is 1/9.** A probability is a possibility. The chance that an event will occur is indicated. The only possible range for an event’s probability is between 0 and 1, with 0 denoting that the event is unlikely to occur and 1 denoting certainty that it will occur.

It is more likely that an event will occur or not, depending on how likely it is, depending on how unlikely it is. The probability of an event is therefore equal to the ratio of favourable outcomes to all possible outcomes. It is indicated by a parenthesis, P(Event).

**P(Event) = N (Favourable Outcomes) / N (Total Outcomes)**

Table of content

## Probability of Getting a Sum of 9

Probability refers to the likelihood or chance that a particular event or outcome will occur. It is typically expressed as a number between 0 and 1, where 0 represents impossibility (an event will not occur) and 1 represents certainty (an event will definitely occur).

Remember that if an event A’s probability of occurring is 1/3, its probability of not occurring is 1-P(A), or 1- (1/3) = 2/3.

**Solution:**

The **number of possible results while throwing two dice is 6×6 = 36.**

Sample space is composed of the following elements: [ (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) ].

As a result, the four pairs that have a sum of nine are (3, 6) (4, 5) (5, 4) and (6, 3).

Total outcomes =36

Favourable outcomes = 4

Probability of obtaining the sum of 9 is determined by the ratio of favourable outcomes/ total outcomes (4/36 = 1/9).

P(sum of 9) = 1/9

**Summary:**

## In a single throw of two dice, what is the probability of getting a sum of 9?

The probability of getting a sum of 9 when two dice are thrown simultaneously is 1/9. When two dice are thrown simultaneously, each die has 6 possible outcomes, ranging from 1 to 6. To determine the probability of obtaining a sum of 9, we need to find the number of favourable outcomes and divide it by the total number of possible outcomes.

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