Question

. A student decides to run a simulation of rolling an even number with a single die. Use the simulat results from 20 attempts to estimate the probability, then compare your estimation with the theoretical probability.
1 5 3 2 3 6 5 6 3 3 4 4 1 3 6 5 3 2 2 6

Answer 1

Answer:

Probability of observed is less that probability of theoretical of getting an even  number.

Step-by-step explanation:

Given : A student decides to run a simulation of rolling an even number with a single die.

Outcomes - 1 5 3 2 3 6 5 6 3 3 4 4 1 3 6 5 3 2 2 6

To find : Use the simulate results from 20 attempts to estimate the probability, then compare your estimation with the theoretical probability?

Solution :

First we make the frequency distribution table,

X    Frequency

1         2  

2         3

3         6

4         2

5         3

6         4

Total - 20

Now, The observed probability of getting an even number.

Favorable outcomes of number appeared even = 3+2+4=9

Total  number of outcome = 20

Probability of getting even number is $P=\frac{9}{20}=0.45$

Then, Theoretical probability of getting an even number.

Favorable outcome = 3

Total  number of outcome = 6

Probability of getting even number is $P=\frac{3}{6}=\frac{1}{2}=0.5$

As 0.45<0.5 , Observed < Theoretical

We simulate that probability of observed is less that probability of theoretical of getting an even  number.

Answer 2

Rolling a single die student gets the  row

1 5 3 2 3 6 5 6 3 3 4 4 1 3 6 5 3 2 2 6,

where numbers

• 1, 5, 3, 3, 5, 3, 3, 1, 3, 5, 3 are odd;
• 2, 6, 6, 4, 4, 6, 2, 2, 6 are even.

Here are 10 odd numbers and 10 even numbers. Then the experimental probability of rolling an even number is

$Pr_{experimental}(\text{Even Number})=\dfrac{10}{20}=0.5.$

Now count the theoretical probability of rolling an even number. A die has 6 numbers: 1, 2, 3, 4, 5, 6. Three of them are even and three of them are odd. Then the theoretical probabilty is

$Pr_{theoretical}(\text{Even Number})=\dfrac{3}{6}=0.5.$

Answer: both probabilities are the same