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## How many events occur in sample space if we take three dice?

Possible Outcomes and Sums

Just as one die has six outcomes and two dice have 6^{2} = 36 outcomes, the probability experiment of rolling three dice has 6^{3} = **216 outcomes**.

## What is the sample space when two dice are thrown?

We know that in a single thrown of two die, the total number of possible outcomes is (6 × 6) = **36**. Let S be the sample space. Then, n(S) = 36. ⇒ odds in favour of E_{1} = P(E_{1})/[1 – P(E_{1})] = (1/9)/(1 – 1/9) = 1/8.

## How many outcomes would there be in the sample space for rolling 3 dice and flipping 2 coins?

Flipping three coins: Each coin has 2 equally likely outcomes, so the sample space is 2 • 2 • 2 or **8 equally likely outcomes**. Rolling a six-sided die and flipping a coin: The sample space is 6 • 2 or 12 equally likely outcomes.

…

First coin | Second coin | outcome |
---|---|---|

T | T | TT |

## How many events are in a sample space?

In fact for a sample space containing 2 possible outcomes Ω={a,b}, the event space contains **4 events**, F={a,b,ab,∅}. In general, for a sample space containing n possible outcomes, the event space is the power set of the sample space, so contains 2n events.

## What is the probability of 3 dice?

Two (6-sided) dice roll probability table

Roll a… | Probability |
---|---|

3 | 3/36 (8.333%) |

4 | 6/36 (16.667%) |

5 | 10/36 (27.778%) |

6 | 15/36 (41.667%) |

## How many sample points are in the sample space when a pair of dice is thrown once?

When a dice is thrown, there are **six possible outcomes**, i.e., Sample space (S) = (1, 2, 3, 4, 5, and 6). When a coin is tossed, the possible outcomes are Head and Tail. So, in this case, the sample space (S) will be = (H, T). When two coins are tossed, there are four possible outcomes, i.e., S = (HH, HT, TH, TT).

## When a dice is thrown the number of sample point in the sample space are?

For sample space of A, we look for total outcomes when the die is rolled in 1, 2, 3, 4, 5, and **6**. In this case, numbers greater than 4 are 5 and 6. Hence, the sample space of A consists of just 5 and 6.

## What is the probability of flipping heads and rolling a three?

N=3: To get 3 heads, means that one gets only one tail. This tail can be either the 1st coin, the 2nd coin, the 3rd, or the 4th coin. Thus there are only 4 outcomes which have three heads. The probability is **4/16 = 1/4**.

## When rolling 3 dice and 3 coins The total number of outcomes is?

Solution: Three different dice are thrown at the same time. Therefore, total number of possible outcomes will be 6^{3} = (6 × 6 × 6) = **216**.