Classical Probability Flashcards

Probability Experiment

• A process that produces random outcomes; examples include flipping a coin, tossing dice, or drawing a raffle ticket.

Outcome

• The individual result possible from a probability experiment.

Sample Space

• All mutually exclusive outcomes of an experiment; also referred to as the probability space.

Event

• A subset of outcomes from the sample space, consisting of one or more possible results.

Thought Experiment

• An abstract scenario that does not require an actual experiment to analyze outcomes.

Probability of an Event

• Calculated as the number of favorable outcomes divided by the total number of outcomes in the sample space.

Sample Space of Flipping a Coin 3 Times

• There are 8 possible combinations of outcomes when a fair coin is flipped three times.

Outcome of Flipping a Coin Once

• The result can be either heads or tails.

Example of a Probability Experiment

• Drawing a number from a hat containing 1 to 10 has ten possible outcomes, with specific events like drawing an even number (2, 4, 6, 8, or 10).

Tree Diagram

• A systematic way to organize outcomes in experiments with several stages for clarity in representation.

Subjective Probability

• An educated guess about the likelihood of an event occurring, influenced by the estimator’s expertise.

Empirical Probability

• Derived from observed data, calculated as the number of times an event occurs divided by the total number of trials.

Rounding Rule

• Present probabilities as exact fractions or decimals rounded to three digits; small probabilities may be rounded to the first nonzero digit.

Law of Large Numbers

• Suggests that as the number of trials increases, the empirical probability will approach the true probability.

Classical Probability

• The most precise type of probability calculated by considering all possible outcomes, defined by n(E) over n(S).

Probability Classifications

• Subjective: Based on educated guess (e.g., teacher predicting class grades).
• Empirical: Based on statistics from observed data (e.g., optometrist's estimate from local school data).
• Classical: Relies on known outcomes (e.g., probability of winning in bingo).

Outcomes When Tossing a Coin

• There are two outcomes: heads and tails.

Outcomes When Rolling a Die

• For rolling an even number with a 6-sided die, three favorable outcomes exist: rolling a 2, 4, or 6.

Probability of Flipping Two Heads in 3 Coin Flips

• There are three favorable outcomes (HHT, HTH, THH) and a total of eight outcomes; probability is calculated as 3/8 or 0.375.

Probability of Flipping at Least Two Heads in 3 Flips

• There are four favorable outcomes (HHT, HTH, THH, HHH) resulting in a probability of 4/8 or 50%.

Drawing a Spade from a Deck

• There are 13 spades in a deck of 52 total cards, yielding a probability of 13/52 or 0.25.

Drawing a Two or a Queen from a Deck

• Eight possible outcomes exist (4 twos and 4 queens) out of 52 cards, leading to a probability of 8/52 or approximately 0.1539.