Question

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

Of the twenty times in this experiment the following are prime (3,5,2,7,3,7,2,2,7,3,3,5) or 12 of the twenty
12/20 = 6/10  = 60%
So 60% is the experimental probabilty.

The theoretical probability given that there are four prime numbers (2,3,5,7) out of 8 on the dice should be 50%  because 1/2 of the numbers are prime.

The experimental probability is 10% more than the theoretical probability
60% - 50% = 10%

Answer 2

-- There are eight (8 x 20) = 160 total possible outcomes.

-- Prime numbers were showing on 12 of the outcomes.

-- The experimental probability was ( 12 / 160 ) = 0.075  =  7.5%

-- This is not right at all !   I think the problem lies in the way
the total number of possible outcomes is defined. 
Let's try it this way:

-- The number of possibilities on each roll is two:  'prime' or 'not prime'.

-- In 20 rolls, there are (20 x 2) = 40 possible outcomes.

-- In this experiment, primes came up 12 times, so the experimental probability
of rolling a prime was  (12 / 40) = 0.3  =  30%.  I like that a lot better.   

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-- Four of the eight faces of the die are marked with prime numbers.
(They are,  2,  3,  5, and  7.)

-- So there is a  (4/8) = 50% theoretical probability of a prime number
showing after every roll, or 50% of any number of rolls.

-- The experimental probability was not "more than" the theoretical probability.
In fact it was  20  percentage points less.

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I'm not comfortable with this whole answer.
But 5 points is not a ton of 'em, so I'll leave
it here for discussion ... a 'target' as it were,
on which others may draw a bead, and utterly
demolish it.          Show me what you got !

========================================

3 minutes later:  Bobeld has already done it.

Anybody else ?