the rolling dice of life a selection of poems

The condition probability refers to the probability of event A happening under the condition that event B has already happened. It is recorded as P(A| B)。The following is an example analysis of the probability of dice rolling. Suppose we have two dice. Event A is that the sum of the two dice is 8, and Event B is that the first die rolls a 3. First, calculate the probability of event A without any conditions. There were a total of 6×6 = 36 possibilities for the outcome of the two dice. There are five cases where the sum of points is 8:(2,6),(3,5),(4,4),(5,3), and (6,2), so P(A)=5/36. Then, the probability of event B is calculated. The probability of the first die rolling a 3 is 1/6, which is P(B)=1/6. The only situation where both events A and B occur at the same time is (3,5), so P(A Empyrean B)=1/36. According to the formula P(A| B)=P(A Empyrean B)/P(B). Under the condition that the first die rolls a 3, the probability of the sum of the two dice points being 8 is P(A| B)=(1/36)/(1/6)=1/6。 For example, Event C was the difference between the two dice being 1, and Event D was the second die rolling a 4. Similarly, P(C) was first found. There were 10 cases where the difference between the points was 1:(1,2),(2,3),(3,4),(4,5),(5,6),(2,1),(3,2),(4,3),(5,4), and (6,5), so P(C)=10/36. The probability of event D is P(D)=1/6. There are two cases where events C and D occur at the same time: (3,4) and (5,4), so P(C Empyrean D)=2/36. Under the condition that the second die rolls a 4, the probability of the difference between the two dice being 1 is P(C| D)=(2/36)/(1/6)=1/3。 In short, when calculating the conditioned probability of rolling the dice, the key was to clarify the relationship between the events, separately calculate the probability of the event occurring alone and the probability of them occurring at the same time, and then use the conditioned probability formula to calculate. Hurry up and click on the link below to return to the super classic "Lord of the Mysteries"!

Rolling dice was a classic example of probability. For a single standard die, because it had six sides, each marked with the six numbers 1, 2, 3, 4, 5, and 6, the chances of each number appearing were equal. Therefore, when throwing a single die, the probability of any number appearing in the result was 1/6. When there were multiple dice involved, the probability calculation would be more complicated. Take two dice as an example, if you consider the size of the dice,(1 - 6 is small, 7 - 12 is big), because there are a total of 6×6 = 36 combinations of the number of points on the two dice. Among them, there are 15 cases where the sum is 1 - 6 (small), and there are 21 cases where the sum is 7 - 12 (big). However, since it is impossible for the two dice to appear, the actual probability of small appearing is 5/11 (about 45.45%), and the probability of big appearing is 6/11 (about 54.55%). If there were three dice, each die would have six situations, and there would be a total of 6x6x6 = 216 combinations. For example, if one calculated the probability of rolling a big die, there would be three kinds of big situations (namely, 4, 5, and 6 points) for each die. There were a total of 3×3×3 = 27 kinds. Therefore, the probability of a big situation appearing was 27 × 216 = 1/8. Similarly, the probability of a small situation appearing was also 1/8. The probability of a leopard appearing (three dice with the same number of points, such as 111, 222, etc.) was 6 × 216 = 1/36. In addition, in theory, if the structure of the die was uneven, for example, the dots were hollowed out, and the six small round pits on the six dots were lighter than the one on the opposite side, then the probability of the six appearing would be greater than the one. However, in the ideal standard die situation, the probability of each number was 1/6. At the same time, there were many other situations in the probability calculation of dice rolling, such as the probability calculation of the sum of two dice numbers being odd, which could be solved by different probability methods (such as the step-by-step probability calculation method in junior high school or the combination knowledge method in high school). Hurry up and click on the link below to return to the super classic "Lord of the Mysteries"!

The following was a handwritten mathematical report about the possibility of rolling the dice: ** I. Title ** "Exploring the mystery of the possibilities in dice rolling." ** 2. Section content ** 1. ** Basic Concepts ** - The die was a six-sided dice, and each side was marked with the numbers 1 - 6. When we roll a die, the probability of each number appearing is equal. This is based on the concept of equal probability events. For example, the probability of rolling 1 is 1/6, because there are six possible outcomes, and 1 is only one of them. 2. ** The result of the combination of two dice ** - When two dice were rolled, the combination of the results could be expressed in a table. For example, if the first die rolls 1, the second die may roll 1 - 6, so there are six combinations of (1,1),(1,2),(1,3),(1,4),(1,5), and (1,6). Similarly, when the first die rolled a 2, there were also six combinations, and so on, there would be a total of 6×6 = 36 different combinations. - The sum of the two dice points ranged from 2 (1+1) to 12 (6+6). Among them, there were six combinations with a sum of 7, namely (1/6),(2,5),(3,4),(4,3),(5,2), and (6,1). Therefore, the probability of rolling two dice with a sum of 7 was 6/36 = 1/6. 3. ** Calculation of probability ** - Calculating the probability that the sum of the two dice points is even. First of all, there were two situations where the sum of two dice points was even: odd + odd or even + even. - The probability of the first die rolling an odd number (1, 3, 5) is 3/6 = 1/2, and the probability of the second die rolling an odd number is also 1/2. Then the probability of both dice rolling an odd number is 1/2×1/2 = 1/4. - Similarly, the probability of the first die rolling an even number (2, 4, 6) is 1/2, and the probability of the second die rolling an even number is also 1/2, so the probability of both dice rolling an even number is 1/2×1/2 = 1/4. - Therefore, the probability of rolling two dice with an even number is 1/4+1/4 = 1/2. 4. ** Practice and Expansion ** - The application in the game: Many tabletop games use the mechanism of rolling dice. For example, in the game Monopoly, the number of steps forward is determined by rolling the dice. This involves the probability of the appearance of the non-synchronized number. - Connection with life: In some lottery activities, if the winning number is determined by rolling the dice, the probability knowledge of rolling the dice needs to be used to determine the probability of winning. At the same time, this could also be extended to areas such as risk assessment. For example, in the insurance industry, for some random events, it could be compared to the probability model of rolling dice to conduct risk assessment. Hurry up and click on the link below to return to the super classic "Lord of the Mysteries"!

In the case of two dice, according to probability theory, the probability of each sum was different. There was only one possibility for the sum to be 2 (1 + 1), and there were six possibilities for the sum to be 7 (1 + 6, 2 + 5, 3 + 4, 4 + 3, 5 + 2, 6 + 1). Therefore, the possibility of the sum being 7 was the highest. The possibility of the sum being 2 and 12 (6 + 6) was the lowest, because there was only one combination that could get these two sums. In a large number of dice throwing experiments, the number of times the sum was 7 was the most, and the number of times the sum was 2 and 12 was the least. For the case of three dice, the total number of points ranged from 3 to 18. The closer to the two sides, the lower the probability of appearing. The situation with the highest number and probability should appear in the middle position, such as 9, 10, 11, and 12. The probability of these points appearing could be calculated separately. When calculating, it was necessary to consider the situation where the three points in the point combination were different and the same points existed. For example, when calculating the probability that the sum of the points is 9,(1;2;6),(1;3;5), and (2;3;4) are the three points that are different,(2;2;5),(3;3;3), and (4;4, 1) are the same points, and when they are all different, the three points need to be completely arranged. Hurry up and click on the link below to return to the super classic "Lord of the Mysteries"!

1. For a single die, the probability of rolling a 6 is 1/6. - Consider the case where two people roll the dice to get a 6 first. This can be calculated by calculating the probability that neither of them rolled a 6 and then deducting this probability from 1. - Let the probability of the first person not rolling a 6 on the first roll of the die be <p>(P1 = 5/6>), and the probability of the second person not rolling a 6 on the first roll of the die be <p>(P2 = 5/6>). - Then the probability of both players failing to roll a 6 on the first try is [P = P1> times P2 =(5/6)> times(5/6) = 25/36]. - Therefore, the probability of one of the two people rolling a 6 first is 1 - 25/36 = 11/36. Hurry up and click on the link below to return to the super classic "Lord of the Mysteries"!