Question

we will roll a standard six-sided die and try to estimate the probability that each number will come up. If it is a fair die, each number should come up 1/6th of the time.

1. Collecting the data

Put a die in a cup and roll it 30 times. With each roll, record what value came up and list the totals in the table below.
For each number the Relative frequency = # of times the number occurs / # of tosses is your estimate of the probability that the die will land each number.

Given that the die is fair, we would expect each value to come up 30/6 = 5 times. Did that occur?

Enter your results into the table on the board to get a set of frequencies for your first 30 rolls. Repeat the process 3 more times and enter the results in the table below. After each set, make a mental note of how the distribution has changed. After all of the tolls, calculate the overall totals and overall relative frequencies.

	Value of1	2	3	4	5	6
Frequency of each value for First set of 30 rolls
Frequency of each value for Second set of 30 rolls
Frequency of each value for third set of 30 rolls
Frequency of each value for Fourth set of 30 rolls
Total
Relative Frequency

2. Analyzing the data and drawing conclusions.
a. Do the frequencies of each number appear to be converging to equal ratios (i.e. is the relative frequency about

1/6th). Using repeated experiments to estimate probability is called Empirical probability. The approach of assuming each value is equally likely is a case of classical probability.

Answer 1

Rolling of dice for 30 times in 4 sets

Given that the die is fair, we would expect each value to come up 30/6 = 5 times. Did that occur?

It occurred very close to the expected results.

Do the frequencies of each number appear to be converging to equal ratios (i.e. is the relative frequency about

1/6th). Using repeated experiments to estimate probability is called Empirical probability. The approach of assuming each value is equally likely is a case of classical probability.

Relative frequency = Total/120
(120 since we have 30 attempts done 4 times)

The frequency of 1/6 is equal to 0.167. We in our experiment we get the probability of each event very close to the expected probability.

If we increase the number of repeated sets, we will be able to approach the required probability.