Answer to Question #216700 in Statistics and Probability for sai

Question

a.

Explain how you could use the random number table shown below to simulate rolling a fair​ six-sided die. Assume you are interested in the probability of rolling a 4.

b.

Using the random number table​ below, report the empirical probability of rolling a 4 on the​ six-sided die from part​ a, and compare it with the theoretical probability of rolling a 4.

1​, 5​, 4​, 9​, 1​, 3​, 3​, 7​, 6​, 2  

4​, 5​, 9​, 6​, 8​, 5​, 2​, 4​, 4​, 8

a. Which of the following is the best explanation on how to use the random number table to simulate rolling the​ die?

Use all the numbers in the random number table.

b. The empirical probability of rolling a 4 is and The theoretical probability of rolling a 4 is

Compare the empirical probability of rolling a 4 with the theoretical probability of rolling a

Answer 1

(a)

Steps for simulation:

 Step 1: State the problem or describe the experiment [rolling a fair six-sided die]

 Step 2: State the assumptions [We are interested in getting 4 as outcome]

Step 3: Assign digits to represent outcomes [Outcomes = 1,2,3,4,5,6]

 Step 4: Simulate many repetitions.[Repeat experiment 20 times ]

 Step 5: State your conclusions.[All the outcomes are in the table .]

(b) from table we obtained , the empirical probability = $\dfrac{4}{20}=\dfrac{1}{5}$

and theoretical probability = $\dfrac{1}{6}$

So, in this case empirical probability is greater than theoretical probability.

(a) Use the numbers 1,2,3,4,5 and 6 to represent the outcomes and ignore 0 and 7-9

(b) from above experiment 4 appears 4 times out of 20.

Hence, the empirical probability of rolling a 4 is equal to $\dfrac{4}{20}=\dfrac{1}{5}$

As theoretically there are 6 digits that can appear on rolling and 4 is one of them

Hence theoretical probability of rolling a 4 is =1/6