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

By Aina Parasher|Updated : May 17th, 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)

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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 6x6 = 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: