Rolling two six-sided dice: Each die has 6 equally likely outcomes, so the sample space is 6 • 6 or 36 equally likely outcomes. Flipping three coins: Each coin has 2 equally likely outcomes, so the sample space is 2 • 2 • 2 or 8 equally likely outcomes.

## How many outcomes would there be in the sample space for rolling 3 dice and flipping 5 coins?

1. The sample space of a fair coin flip is {H, T}. The sample space of a sequence of three fair coin flips is all **23 possible** sequences of outcomes: {HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}.

## How many possible outcomes are there when you roll 3 die and flip two coins?

The number of **different outcomes** when **three coins** are tossed is **2** × **2** × **2** = 8. All eight **possible outcome** are HHH, HHT, HTH, HTT, THH, THT, TTH, and TTT. Step **2**. **There** are four **possible** events: 0 heads, 1 head, **2** heads, and **3** heads.

## What is the sample space when rolling 3 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 outcomes can you have from rolling 2 dice and flipping 2 coins?

As you are tossing the 2 coins simultaneously there are only 3 discernible outcomes for the two coins, 2 heads, 2 tails, or 1 head 1 tail. Combined with these three discernible outcomes there are 6 possible outcomes for the toss of the die. So the total number of possible (discernible) outcomes is **18**.

## What is the probability of rolling a 2 or a 3 on a six sided die?

Probability of rolling a certain number or less with one die

Roll a…or less | Probability |
---|---|

1 | 1/6 (16.667%) |

2 | 2/6 (33.333%) |

3 | 3/6 (50.000%) |

4 | 4/6 (66.667%) |

## How many outcomes would there be in the sample space for rolling 5 dice and flipping 2 coins?

** How many outcomes are in the event where nobody rolls a six? If they can’t roll a six, there are 5 other numbers to roll, and either coin-flip is still allowed. So each person has 2×5=**10 possible outcomes**. Since there are 5 people, there are 105 possible outcomes.