# A die is thrown 4 times. What is the probability of the sum of all the throws being equal to 6.

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### 2 Answers

A die is a cube with the numbers 1 to 6 on its faces. When a die is thrown 4 times there are six ways that it can land each time. The total number of possibilities when the die is thrown 4 times is 6^4 = 1296.

To get a sum of 6 from all the 4 throws of the die, the numbers that need to turn up for the throws is either (1, 1, 2, 2) or (1, 1, 1, 3).

There are 4 ways of getting the numbers as (1, 1, 1, 3) and 6 ways of getting (1, 1, 2, 2). The sum of the numbers that turn up can be 6 in 10 different ways.

This gives a probability that the sum of the numbers that turn up when a die is thrown 4 times being 6 as 10/1296 = 5/648

**The required probability is 5/648**

There are 6 faces on a die, which gives you 6 numbers each of the 4 die could potentially land on. This gives you 1296 *total* combinations (6^4).

In order for the sum to be 6, you would either need the combination 1, 1, 1, & 3 OR 1, 1, 2, & 2. There are 10 possible ways to get these combinations, depending on which number is rolled first, giving you a probability of 10/1296 or **5/648**.