Question

Frequent 90%

Likely 65% - 90%

Possible 35% - 64%

Unlikely 10% - 34%

Rare 10%

f. Based on your dice rolls, what is the experimental probability of rolling a three, out of 18 rolls? Also, list the likelihood scale term from the table above.

	Percent Probability
Experimental Probability (Rounded to the Nearest Whole Percent)	?
Likelihood Scale Term	?

Show your work here:

With regard to the likelihood scale terms for each, how did this differ from both the theoretical and empirical probabilities?

?

Answer 1

The binomial distribution formula is:

b(x; n, P) = _nC_x * P^x * (1 – P)^{n – x}

Where:
b = binomial probability
x = total number of “successes” (pass or fail, heads or tails etc.)
P = probability of a success on an individual trial
n = number of trials

as per theoretical probability probability of getting atleast 1 three out of 18 rolls is

What’s the probability of any given trial being a success? (p) = 1/5

How many trials are there total? (n) = 18

How many trials were successful? (min) = 1

How many trials were successful? (max) = 18

probability = 0.981985601490519.

that is 98.2% theoretically

but possibly on doing experiment we may get 1 three, 2 threes or more than 2 upto 18.

and that possiblity is not fixed it may be varies from 0% to 100%.

theoretically likelihood scale term is frequent.

but practically it may be ferquent or likely or any other.

hence this is the difference.

The theoretical probability is what you expect to happen, but it isn't always what actually happens.