Question

Need help please 20 PTS

Answer 1

Answer:

The experimental probability of rolling a prime number is 75%, which is 25% more than the theoretical probability.

Step-by-step explanation:

Given : A special 8-sided die is marked with the numbers 1 to 8. It is rolled 20 times with these outcomes :

3 4 5 2 7 1 3 7 2 6 2 1 7 3 6 1 8 3 5 6

To find : The experimental probability of rolling an odd number is  ____%, which is  ____% more than the theoretical probability?

Solution :

1) Theoretical probability

Sample - 1,2,3,4,5,6,7,8

Rolling a prime number from sample is 2,3,5,7=4

Total sample = 8

The theoretical probability of rolling a prime number is

$P=\frac{4}{8}=\frac{1}{2}=0.5$

In percentage, 0.5=50%

2) The experimental probability

Outcomes - 3 4 5 2 7 1 3 7 2 6 2 1 7 3 6 1 8 3 5 6

The outcomes that are prime are:

{ 3   2    5    7    1    3    7    2    2    1    7    3    1    3    5}

Number of favorable outcomes= 15

Total number of outcomes = 20

Now, The experimental probability of rolling a prime number is

$P=\frac{15}{20}=\frac{3}{4}=0.75$

In percentage, 0.75=75%

As 75%-50%=25%

Therefore, The experimental probability of rolling a prime number is 75%, which is 25% more than the theoretical probability.

Answer 2

Answer:

The experimental probability of rolling an odd number is  

55%, which is  

5% more than the theoretical probability.

Step-by-step explanation:

3 4 5 2 7 1 3 7 2 6 2 1 7 3 6 1 8 3 5 6

The odd outcomes are in bold below:

3 4 5 2 7 1 3 7 2 6 2 1 7 3 6 1 8 3 5 6

There were 20 rolls of the die. 11 of the 20 rolls were odd.

experimental probability of rolling an odd number = 11/20 = 55%

The die has 4 even numbers and 4 odd numbers. The theoretical probability of rolling an odd number is

theoretical probability of rolling an odd number = 4/8 = 1/2 = 50%

The experimental probability is 5% more than the theoretical probability.

Answer: The experimental probability of rolling an odd number is  

55%, which is  

5% more than the theoretical probability.