Question 1

What is theoretical probability?

Accepted Answer

Theoretical probability is calculated by taking the ratio of the number of favorable outcomes to the total number of equally likely possible outcomes in a sample space:

P(A) = \frac{ ext{favorable}}{ ext{total}}

.

Question 2

How do you find the probability of a complementary event?

Accepted Answer

The complement rule states that

P(A) = \frac{ ext{favorable}}{ ext{total}}

, where

\overline{A}

denotes the complement ("not

A

"). Because an event either happens or does not happen (

P(A) + P(\overline{A}) = 1

), subtract the probability of the event from 1.

Question 3

What is the arithmetic mean?

Accepted Answer

The arithmetic mean is the average of a dataset, calculated by summing all values and dividing by the total count of values:

P(A) = \frac{ ext{favorable}}{ ext{total}}

.

Question 4

How does the Balance Beam illustrate the mean?

Accepted Answer

On a number line, if each data point acts as a unit weight, the mean is the exact fulcrum (center of gravity) where the total leftward distance equals the total rightward distance.

Statistics & Probability: Exam