Question

Determine whether the following probabilities are best categorized as subjective, empirical, or classical probabilities.

a. Before flipping a fair coin, Sunil assesses that he has a 50% chance of obtaining tails. Subjective probability Empirical probability Classical probability
b. At the beginning of the semester, John believes he has a 90% chance of receiving straight A’s. Subjective probability Empirical probability Classical probability
c. A political reporter announces that there is a 46% chance that the next person to come out of the conference room will be a Republican, since there are 80 Republicans and 93 Democrats in the room. Subjective probability Empirical probability Classical probability

Answer 1

a) Classical. This is because there are 2 sides and 1/2 = 0.50 = 50% is the chance of landing on tails. Classical probability is also known as theoretical probability.

b) Subjective. This is based off John's belief and his gut feeling. There doesn't seem to be any empirical data to back him up, unless he's looking back at previous semesters.

c) Empirical. When you have a finite set of data and you compute the probability based on it like what we're doing here, we're computing empirical probability. Another example would be that if you flipped a coin 30 times and got 17 heads, then the empirical probability of getting heads is 17/30 = 0.5667 approximately. Note how this is slightly different from the theoretical probability 0.50