Probability Lecture Flashcards

These flashcards cover key concepts and definitions from the lecture on probability.

The probability of event A is written as __.

P(A) and is a number between 0 and 1.

If P(A) = 0, this means __.

Event A never occurs.

If P(A) = 1, this means __.

Event A always occurs.

Classical probability is based on __ and the assumption that all outcomes are equally likely.

logic

In classical probability, the formula is __.

P(A) = Number of favorable outcomes / Total number of possible outcomes.

Empirical probability is based on __ from experiments or past observations.

data

The formula for empirical probability is __.

P(A) = Number of times A occurred / Total number of trials (n).

As sample size increases, P ̂ (A) __.

converges to the theoretical probability.

The Law of Large Numbers states that as the number of trials increases, the __ of an event converges to its theoretical probability.

experimental probability

The complement of an event A is denoted as __ or 'not A'.

A^C

For mutually exclusive events, the probability of A and B occurring together is __.

P(A ∩ B) = 0.

If A and B are mutually exclusive, P(A ∪ B) = __.

P(A) + P(B)

Conditional probability is denoted as __.

P(A|B)

The formula for conditional probability is __.

P(A|B) = P(A ∩ B) / P(B) where P(B) > 0.

The probability that someone swims and does not get an ear infection is __.

0.08.

The Complement Rule states that P(A c | B) = __.

1 - P(A|B)