Answer to Question #216696 in Statistics and Probability for sai

Question

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 2.

b.

Using the random number table​ below, report the empirical probability of rolling a 2 on the​ six-sided die from part​ a, and compare it with the theoretical probability of rolling a 2.

1​, 8​, 4​, 6​, 2​, 0​, 1​, 8​, 8​, 6  

2​, 9​, 6​, 2​, 6​, 2​, 4​, 8​, 1​, 1

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

Use the numbers​ 1, 2,​ 3, 4,​ 5, and 6 to represent the outcomes and ignore 0 and​ 7-9.

b. The empirical probability of rolling a 2 is

The theoretical probability of rolling a 2 is

Compare the empirical probability of rolling a 2 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 2 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 2 appears four times out of 20.

Hence, the empirical probability of rolling a 2 is equal to $\dfrac{4}{20}=\dfrac{1}{5}$

As theoretically there are 6 digits that can appear on rolling and 2 is one of them

Hence theoretical probability of rolling a 2 is =1/6