Question

HELP PLEASE WILL FAN AND MEDAL!!!
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

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

Answer 1

@welshfella

Answer 2

The probability of rolling a number is the number of way that number can be rolled divided by the total number of outcomes.

Answer 3

There are 8 faces numbered 1 through 8. That means there are 8 different possible outcomes.

Answer 4

How many of those outcomes are prime numbers?

Answer 5

@mathstudent55 4 of them are prime numbers.

Answer 6

1, 2, 3, 4, 5, 6, 7, 8
2, 3, 5, 7 are prime
You are correct.

Answer 7

There are 4 desired outcomes (2, 3, 5, 7) and there are 8 total possible outcomes.
What is the theoretical probability of rolling a prime number?

Answer 8

@mathstudent55 would it be 0.5%?

Answer 9

You are on the right track, but you need to be careful with numbers.

Theoretical probability:
p(rolling a prime number) = 4/8 = 0.5 = 50%

0.5% is incorrect.
It's either 50% or 0.5

Ok?

Answer 10

yah ok thank

Answer 11

Both 50% and 0.5 probability mean half, which makes sense since half of the total number of outcomes is prime numbers, 4 out of 8.

Answer 12

The theoretical probability of rolling a prime number is 0.5
Now you need the experimental probability.
You need to find the probability based on the actual experiment.
How many prime numbers were rolled out of a total of how many rolls of the die?

Answer 13

12 prime numbers were rolled in the experiment.

Answer 14

which is = to 20%

Answer 15

Yes, 12 numbers were prime.
How many total rolls of the die?

Answer 16

20 rolls

Answer 17

do divide 12 by 20 and i got 60%

Answer 18

\(3 ~4 ~5 ~2 ~7 ~1 ~3 ~7 ~2 ~6 ~2 ~1 ~7 ~3 ~6 ~1 ~8 ~3 ~5 ~6\) <--- 20 rolls

\(\color{red}{3} ~4 ~\color{red}{5} ~\color{red}{2} ~\color{red}{7} ~1 ~\color{red}{3} ~\color{red}{7} ~\color{red}{2} ~6 ~\color{red}{2} ~1 ~\color{red}{7} ~\color{red}{3} ~6 ~1 ~8 ~\color{red}{3} ~\color{red}{5} ~6\) <--- 12 prime numbers

Answer 19

Correct.

Experimental probability:
p(roll of a prime) = 12/20 = 0.6 = 60%.

Answer 20

Now the last part.
60% is what percent higher than 50%?

Answer 21

10%

Answer 22

thanks @mathstudent55

Answer 23

You're welcome.