Question

1. classify each statement as an example of classical probability, empirical probability, or subjective probability.

a. the probability that a person will watch the 6 oclock evening news is 0.15.
b. the probability of winning at a chuck - a - luck game is 5/36.
c. the probability that a bus will be in an accident on a specific run is about 6%.
d. the probability of getting a royal flush when five cards are selected at random is 1/649,740.

Explanation:

• Classical probability: It is based on the assumption of equally - likely outcomes. For example, in a standard deck of cards, when calculating the probability of getting a royal flush (a very specific hand in poker), we know the total number of possible 5 - card hands (\(C(52,5)=\frac{52!}{5!(52 - 5)!}\)) and the number of royal flush hands (4, one for each suit). The formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\) is used.
• Empirical probability: It is based on observed data. For instance, if we observe the number of times a bus has been in an accident over a period of time and divide it by the total number of bus trips, we get an empirical probability. But when we say "the probability that a bus will be in an accident on a specific run is about 6%", if this 6% is based on past data (e.g., out of 1000 runs, 60 had accidents), it is empirical.
• Subjective probability: It is based on personal judgment. When we say "the probability of winning at a Chuck - a - Luck game is \(\frac{5}{36}\)", if it is not based on a well - defined equally - likely outcome model (like in a fair die - rolling game where we can calculate probabilities based on the number of sides of the die) but rather on a person's guess or past experience (not in a systematic, equally - likely way), it could be subjective. When we say "the probability that a person will watch the 6 o'clock evening news is 0.15", if it is not based on a large - scale random sample (which would make it empirical) but on a person's hunch (e.g., a news editor's guess), it is subjective.

Answer:

a. Subjective probability
b. Subjective probability
c. Empirical probability
d. Classical probability