Probability from Equal Likelihood to Axioms

The naive definition

Properties that follow from symmetry

The axioms of probability

Why axioms beat intuition

A jar holds 3 red and 5 blue marbles, identical except for color, and one is drawn blind. Does the naive definition of probability apply to the color of the drawn marble?

A fair coin is tossed 4 times. Which expression computes P(at least one tail)?

One card is drawn from a well-shuffled deck. Using inclusion-exclusion, P(ace or heart) = P(ace) + P(heart) - P(ace of hearts). Write the result as a fraction a/b in lowest terms, for example 7/13. Enter the denominator b.

A die is loaded so that $P(6) = 0.5$ and the other five faces are equally likely. What is the probability of rolling a number strictly less than 5? Enter a decimal like 0.4.

An event A is contained in an event B, and P(A) = 0.3 while P(B) = 0.3. What is P(B and not A)? Enter a decimal.

In your own words, state the most important definition, theorem or method of this lesson and explain what it says.