# Frequent question: What is the size of the sample space for rolling 3 6 sided dice?

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## What is the sample space in rolling three dice?

When three dice are rolled sample space contains 6 × 6 × 6 = 216 events in form of triplet (a, b, c), where a, b, c each can take values from 1 to 6 independently. Therefore, the number of samples is 216.

## How many elements are in the sample space of three rolls of a six sided die?

There are therefore 6*6*6=216 possible combinations of the three. Of those, If one is a 4, the other two must be 1s, which means there are three possible combinations to get a six total with one 4.

## What is the probability of rolling a sum of 12 on a six sided dice?

Probabilities for the two dice

Total Number of combinations Probability
10 3 8.33%
11 2 5.56%
12 1 2.78%
Total 36 100%

## What is the probability of rolling 3 dice and them all landing on a 6?

And there are a total of 216 total combinations (6 sided die, three dice, means you calculate this by multiplying 6x6x6). Therefore, the probability is 6/216, or 1/36 when reduced to lowest fraction.

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## What is the probability of rolling a 4 on a 6 sided dice?

Two (6-sided) dice roll probability table

Roll a… Probability
4 3/36 (8.333%)
5 4/36 (11.111%)
6 5/36 (13.889%)
7 6/36 (16.667%)

## What is the probability of rolling a 6 or flipping a coin and getting heads?

Multiply the probability of Heads P(x=H | coin) = 1/2 . The probability of 2 P(x=2 | Die) = 1/6.

## How many total outcomes do you expect to find from rolling 2 dice and flipping a coin?

Explanation: When you flip a coin there are two possible outcomes (heads or tails) and when you roll a die there are six outcomes(1 to 6). Putting these together means you have a total of 2×6=12 outcomes.

## How many outcomes would there be in the sample space for rolling 4 dice?

My initial reaction is to say that the answer is 64, since 4 dice can have 6 outcomes.