DIFFERENCE BETWEEN EXPERIMENTAL AND THEORETICAL PROBABILITY WORKSHEET

Question 1 :

In the experiment of rolling a six faced cube (faces numbered from 1 to 6) for 30 times and find the difference between theoretical and experimental probabilities.

Question 2 :

Could the experimental probabilities ever be exactly equal to the theoretical probability? If so, how likely is it? If not, why not ?

Detailed Answer Key

Question 1 :

In the experiment of rolling a six faced cube (faces numbered from 1 to 6) for 30 times and find the difference between theoretical and experimental probabilities.

Answer : 

Step 1 :

When we roll the cube once, the theoretical probabilities for different outcomes. 

There are 18 possible outcomes in the sample space.

Getting number 1 ---> Theoretical probability  =  1/6

Getting number 2 ---> Theoretical probability  =  1/6

Getting number 3 ---> Theoretical probability  =  1/6

Getting number 4 ---> Theoretical probability  =  1/6

Getting number 5 ---> Theoretical probability  =  1/6

Getting number 6 ---> Theoretical probability  =  1/6

Step 2 : 

When we roll the cube for 30 times, number of times each number will be rolled.

1 : 30 x 1/6  =  5 times

2 : 30 x 1/6  =  5 times

3 : 30 x 1/6  =  5 times

4 : 30 x 1/6  =  5 times

5 : 30 x 1/6  =  5 times

6 : 30 x 1/6  =  5 times

Step 3 : 

When we roll the cube for 30 times, number of times each number will be rolled.

Number 1 : 30 x 1/6  =  5 times

Number 2 : 30 x 1/6  =  5 times

Number 3 : 30 x 1/6  =  5 times

Number 4 : 30 x 1/6  =  5 times

Number 5 : 30 x 1/6  =  5 times

Number 6 : 30 x 1/6  =  5 times

According to theoretical probability, we get each number 5 times in rolling the cube 30 times.

Step 4 : 

Now, let us do the actual experiment and record the results. That is, rolling a cube 30 times. 

From the above table, after simplification, we get the following experimental probabilities for each number. 

Getting number 1 ---> Experimental probability  =  1/5

Getting number 2 ---> Experimental probability  =  2/15

Getting number 3 ---> Experimental probability  =  1/10

Getting number 4 ---> Experimental probability  =  1/5

Getting number 5 ---> Experimental probability  =  7/30

Getting number 6 ---> Experimental probability  =  2/15

Step 5 : 

Look at the results in step 1 and step 4.

How do the experimental probabilities compare with the theoretical probabilities ?

The experimental probabilities are not close to the theoretical probabilities.

But, by performing more trials, we may tend to get experimental results that are closer to the theoretical probabilities.

Question 2 :

Could the experimental probabilities ever be exactly equal to the theoretical probability? If so, how likely is it? If not, why not ?

Answer :

Yes, the experimental probabilities could be exactly equal to the theoretical probabilities, but it is very unlikely.

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