样本空间与事件

Why probability needs a universe of outcomes

Pebble World and events

Describing events precisely

Counting the rooms in the universe

A coin is tossed three times and the sample space lists ordered results such as $HTH$. Which subset is the event not all three tosses agree?

Two cards are drawn one after another from a standard deck and you care about the values in the order drawn. Which sample space is appropriate?

By De Morgan's laws, the event that it is false that (the alarm rings AND the dog barks) equals the event that the alarm does something OR the dog does something. In symbols, $(A \cap B)^c = A^c \,\square\, B^c$ where $\square$ is the union or intersection symbol written as a word, either union or intersection. Enter that word.

A coin is tossed 8 times and the full outcome records every toss in order, like $HTTHHTHT$. How many outcomes does this sample space contain? Enter the integer.

Two dice are rolled and you want the number of outcomes where the sum is NOT 7. Out of the 36 ordered outcomes, how many have a sum different from 7? Enter the integer.

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