If I roll a pair of dice 500 times what sum would appear the most
7 is the most likely outcome
using distinguishable dice, there are 36 possible outcomes
... each of the six faces on a die can pair with the six faces on the other die ... 6 * 6 = 36
twelve of those outcomes result in a sum of 7
... one third of the rolls
To find out which sum would appear the most when rolling a pair of dice 500 times, you can use probability theory and simulate the process through a computer program. Here's an explanation of the steps needed to obtain the answer:
1. Understand the sum possibilities: when rolling a pair of fair six-sided dice, each die can show numbers from 1 to 6. So, the possible sum range is from 2 (1+1) to 12 (6+6).
2. Calculate all possible sums: create a table or list with all possible sums that can occur. For example, the sums 2, 3, 4, ..., 12.
3. Determine the probabilities: for each possible sum, calculate the probability of obtaining that sum when rolling two dice. The probability of rolling a particular sum is equal to the number of ways that sum can be obtained divided by the total number of possible outcomes. For example, to find the probability of rolling a sum of 7, you need to count all the ways you can roll a 7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1), which is 6. Then divide this by the total number of possible outcomes, which is 36 (6 possible outcomes for each die). So, the probability of rolling a sum of 7 is 6/36 or 1/6.
4. Simulate rolling the dice: write a computer program that simulates the process of rolling two dice 500 times. Each roll will produce a sum. Keep track of how many times each sum appears.
5. Analyze the results: after running the simulation, analyze the collected data to determine which sum appeared the most frequently. This will be the sum that appears most often when rolling a pair of dice 500 times.
By following these steps, you can accurately determine which sum is most likely to appear the most frequently when rolling a pair of dice 500 times.