The probability of throwing two dice and obtaining a 4 and a 6 is 1/36. This is because there is only one possible outcome (a 4 and a 6) out of 36 possible outcomes when rolling two dice.

The probability of throwing two dice and obtaining a 4 and a 6 is 1/36. This probability can be calculated by considering all the possible outcomes when rolling two dice. Each die has six faces numbered 1 to 6, so the total number of possible outcomes when rolling two dice is 6 x 6 = 36.

Out of these 36 possible outcomes, only one combination results in obtaining a 4 and a 6. The 4 can appear on the first die and the 6 on the second die, or vice versa. Therefore, there are two equally likely ways to obtain a 4 and a 6: (4, 6) and (6, 4).

To calculate the probability, we divide the number of favorable outcomes (2) by the total number of outcomes (36): 2/36 = 1/18.

A well-known resource, the Encyclopedia Britannica, explains the concept of probability as follows: “Probability, in mathematics, a measure of the likelihood of an event. The probability of throwing two dice and obtaining a specific combination can be calculated by dividing the number of ways to obtain that combination by the total number of possible outcomes.”

Here are some interesting facts related to dice and probability:

- Dice have been used for thousands of years and have been found in archaeological sites dating back to ancient Egypt and Mesopotamia.
- The most common type of dice is a six-sided cube, but dice can also have different shapes and numbers of sides, such as four-sided, eight-sided, or even twenty-sided.
- The study of probabilities and the mathematics behind them was developed by mathematicians like Blaise Pascal and Pierre de Fermat in the 17th century.
- Probability theory is widely used in various fields, including statistics, game theory, physics, and finance.
- Rolling two dice provides a classic example of discrete probability, as the possible outcomes are distinct and countable.
- The probability of rolling a specific number on a single six-sided die is 1/6, as there is only one favorable outcome out of six possible outcomes.
- The probability of obtaining a sum of 7 when rolling two dice is the highest, with 1/6 probability, as there are six favorable outcomes (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) out of a total of 36 possible outcomes.

Table:

Possible Outcomes when Rolling Two Dice:

Die 1 | Die 2 |
---|---|

1 | 1 |

1 | 2 |

1 | 3 |

1 | 4 |

1 | 5 |

1 | 6 |

2 | 1 |

2 | 2 |

2 | 3 |

2 | 4 |

2 | 5 |

2 | 6 |

3 | 1 |

3 | 2 |

3 | 3 |

3 | 4 |

3 | 5 |

3 | 6 |

4 | 1 |

4 | 2 |

4 | 3 |

4 | 4 |

4 | 5 |

4 | 6 |

5 | 1 |

5 | 2 |

5 | 3 |

5 | 4 |

5 | 5 |

5 | 6 |

6 | 1 |

6 | 2 |

6 | 3 |

6 | 4 |

6 | 5 |

6 | 6 |

Remember that these probabilities hold true for fair, unbiased dice.

**Video response to “What is the probability of throwing two dice and obtaining a 4 and a 6?”**

In this video, the speaker explains how to calculate the probability of getting specific sums when rolling two dice simultaneously. They demonstrate the process using a matrix and show that the probability of getting a sum of 7 is 1 out of 6. They then discuss the probabilities of getting a sum greater than 7 and a sum less than 6. The speaker emphasizes the importance of creating a matrix or table to organize the outcomes and explains that counting the favorable outcomes and dividing by the total outcomes gives the probability. They also provide a practice question for viewers to try and encourage them to verify their answer by adding the probabilities of getting a sum less than 7 and a sum greater than 7.

## See more possible solutions

The probability of getting 4, 5 or 6 in the first throw and 1, 2, 3, or 4 in the second throw would be, = P (A) × P (B) = 3 6 × 4 6 =

1 3Therefore, option (B) is the correct answer.

## I am confident that you will be interested in these issues

### What is the probability of rolling 2 dice and getting a 4 or 6?

Hence, the probability of getting a sum of 4 or 6 is 8/36, or 2/9, as desired.

### What is the probability of rolling a 4 and a 6?

Answer: Summary: The probability of rolling a ‘4’ or a ‘6’ on one toss of a standard six-sided die is 1/3.

### What is the probability of rolling two dice and getting and 4?

The reply will be: Answer: The probability of rolling two dice and getting a sum of 4 is 1/12. Let’s find how likely we get a sum of 4 when we roll two dice simultaneously. So, when we roll two dice there are 6 × 6 = 36 possibilities. When we roll two dice, the possibility of getting number 4 is (1, 3), (2, 2), and (3, 1).

### What is the probability of rolling two dice and getting 6 on both of them?

Answer: The probability of a double-six in one throw of two die is 1/36 or 0.028.

### What is the probability of rolling two dice and getting 4?

As a response to this: So, when we roll two dice there are 6 × 6 = 36 possibilities. When we roll two dice, the possibility of getting number 4 is (1, 3), (2, 2), and (3, 1). Probability = The number of favorable outcomes / Total number of possibilities = 3 / 36 = 1/12. Thus, 1/12 is the probability of rolling two dice and getting a sum of 4.

### What happens if two identical dice are thrown simultaneously?

Response will be: If two identical dice are thrown simultaneously (The order of result does not matter. For example, (2, 3) ( 2, 3) and (3, 2) ( 3, 2) are considered same), what is the probability of getting same number on both the dice? Now the reduced sample space is of size = 6 +(62) = 6 + 15 = 21 6 + ( 6 2) = 6 + 15 = 21.

### What are dice throw probabilities?

The answer is: The classic case of exploring dice throw probabilities (dice rolling odds) is to estimate the chance of landing a given sum on the faces of two six-sided dice. In this example, two dice are thrown together and one records their face values, and computes their sum.

### What is the probability of throwing a six with 6 tries?

This means that the probability of throwing at least one six with six tries is 1 – 0.3349 = 0.6651 or 66.51% giving odds of roughly 2/3. In effect, the multiplication in the denominator calculates the sample space whereas the multiplication in the numerator computes the number of unfavourable outcomes in the sample space.

### What is the probability of rolling two dice and getting 4?

So, when we roll two dice there are 6 × 6 = 36 possibilities. When we roll two dice, the possibility of getting number 4 is (1, 3), (2, 2), and (3, 1). Probability = The number of favorable outcomes / Total number of possibilities = 3 / 36 = 1/12. Thus, 1/12 is the probability of rolling two dice and getting a sum of 4.

### How do you calculate the probability of throwing a dice?

Answer will be: For example, throwing a 3 is twice as likely as throwing a 2 because there are two distinguishable ways to get a 3. The probability of getting a given value for the total on the dice may be calculated by taking the total number of ways that value can be produced and dividing it by the total number of distinguishable outcomes.

### How many outcomes are there when you throw two dice?

Answer to this: There are 36 outcomes when you throw two dice. For a single die, there are six faces, and for any roll, there are six possible outcomes. For two dice, you should multiply the number of possible outcomes together to get 6 × 6 = 36. With subsequent dice, simply multiply the result by 6.

### How do you get a number other than 4 on dice?

To be able to get a number other than 4 on either dice, any combination but 4,4 has to be the outcome. Since each possible outcome has a probability of 1/36, the probability of at least one non-four number is 1 – 1/36 or 35/36. To be able to get no four on either dice, the outcome must be not one of the following: