The sample space is the complete set of all possible outcomes for a probability experiment, listed without repetition. It forms the foundation for every probability calculation because the probability of any event is a fraction of the sample space.
Before calculating probability, list every possible outcome. For a die: {1,2,3,4,5,6}. For two coins: {HH,HT,TH,TT}. That's your sample space - the complete menu of what could happen.
Showing a random 20 of 50 problems.
Example 1
easy
How many outcomes are in the sample space for drawing one card from a standard 52-card deck?
Example 2
medium
Two dice are rolled. How many outcomes give a product equal to 12?
Example 3
medium
A coin is flipped, then a 4-sided die is rolled. How many outcomes are in the sample space?Sample space for flipping a coin then rolling a 4-sided die
Example 4
challenge
Two dice are rolled. How many outcomes in the sample space have at least one die showing a 6?Outcomes where at least one die shows a 6 (11 total)
Example 5
easy
List the sample space for rolling a standard six-sided die and flipping a coin simultaneously.
Example 6
medium
Two dice are rolled and we record only the unordered pair (a, b) with a≤b. How many unordered outcomes are in the sample space?
Example 7
hard
A committee chooses a chair and a secretary from 8 people (different people for each role). How many sample-space outcomes are there?
Example 8
medium
A coin is flipped twice. List the sample space where order matters.All ordered outcomes for two coin flips
Example 9
medium
A 4-digit PIN uses digits 0-9 with repetition allowed. How many possible PINs are in the sample space?
Example 10
easy
A coin is flipped 4 times. How many outcomes are in the sample space?
Example 11
easy
List the sample space for the sum when rolling two dice.
Example 12
easy
List the sample space for drawing one ball from a bag with balls labeled A, B, C, D, E.
Example 13
hard
A password is exactly 5 characters chosen from 26 lowercase letters with no repetition. How many passwords are in the sample space?
Example 14
medium
A 4-digit PIN uses digits 0-9 with repeats allowed. How many PINs are in the sample space?
Example 15
challenge
How many outcomes are in the sample space for arranging the letters A, B, C in a row?
Example 16
medium
An outfit is one of 3 shirts and one of 4 pants. How many outfits are in the sample space?
Example 17
challenge
Two cards are drawn from a 52-card deck without replacement and order does not matter. How many outcomes are in the sample space?
Example 18
medium
How many outcomes are in the sample space for flipping a coin and then rolling a die?Sample space for flipping a coin then rolling a die
Example 19
hard
Two dice are rolled. (a) How many outcomes are in the sample space? (b) How many outcomes give a sum of 7? (c) How many outcomes give a sum greater than 10? (d) Which sum is more likely: 7 or greater than 10?
Example 20
hard
A 3-letter code uses letters from {A, B, C, D} with repetition allowed. How many codes are in the sample space, and how many use no repeated letter?