# A single dice is thrown twice. What is the probability that the sum is neither 8 nor 9?

By BYJU'S Exam Prep

Updated on: September 25th, 2023

A single dice is thrown twice, and the probability that the sum is neither 8 nor 9 is 3/4. Probability is equal to the number of total outcomes divided by the number of favorable outcomes. The range of probability is between 0 and 1. To solve this question, one must take into consideration the combinations that will have the sum of 8 or 9 on both rolls of the dice.

## Probability of Sum Being Neither 8 nor 9 on Throw of Dice Twice

The probability of getting a sum that is neither 8 nor 9 upon a roll of dice twice can be calculated by using the following formula –

P(E) = Total number of outcomes/Number of favorable outcomes

One can calculate the probability of an event based on the ratio of the number of total outcomes and the number of favorable outcomes. The probability of an event is always between 0 and 1 with o meaning that an event is impossible to happen and 1 meaning an event is possible.

### Solution

If a dice is rolled twice, we will consider the results of both rolls to know the probability of getting neither 8 nor 9.

So, first, we will know the combinations that will add the sum to 8 –

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

So, the Probability of getting a sum of 8 = 5/36

Similarly, the combinations that will give us the sum of 9 are as follows –

(3, 6), (4, 5), (5, 4), (6, 3)

So, the Probability of getting a sum of 9 = 4/36

Now, to calculate the probability that the sum is neither 8 nor 9 when the dice is rolled two times is –

= 1 – P (sum is either 8 or 9)

=1−(5/36 + 4/36)

=3/4

Hence, on a roll of dice twice, 3/4 is the probability of not getting 8 or 9 as a sum.

Summary:

## A single dice is thrown twice. What is the probability that the sum is neither 8 nor 9?

If a dice is thrown twice, the probability that the sum is neither 8 or 9 is 3/4. For this, the combination of numbers that can give a sum 8 or 9 should be considered based on the outcomes of two dice rolls.

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