Practice Sample Space in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The sample space is the set of all possible outcomes of a random experiment — every outcome that could conceivably occur.
Before you can calculate any probability, you need the complete menu of possibilities. The sample space is that menu—like listing every face of a die or every possible hand in a card game. Missing even one outcome throws off every probability you calculate, because all probabilities must add up to exactly 1 over the full sample space.
Showing a random 20 of 50 problems.
Example 1
challengeFrom 5 people, how many ways to form a committee of 2 with one chair (chair distinguished)?
Example 2
mediumA 4-digit PIN uses digits 0-9, repeats allowed. Size of the sample space?
Example 3
mediumA coin is flipped, then a die is rolled. How many outcomes are in the sample space?
Example 4
mediumYou draw two cards (without replacement) from a -card deck. How many ordered outcomes are in the sample space?
Example 5
easyList the sample space for the sum of two coins counting heads (0, 1, or 2 heads). Are outcomes equally likely?
Example 6
easyThe probabilities of all outcomes in a sample space must sum to what number?
Example 7
easyHow many outcomes are in the sample space for choosing a month of the year?
Example 8
easySample space size for flipping two coins?
Example 9
easyHow many outcomes when rolling two distinct dice?
Example 10
mediumA spinner has 8 equal sectors. P(landing on a multiple of 3)?
Example 11
mediumA spinner has sections with probabilities . What must the missing probability be?
Example 12
easyA bag contains one red, one blue, and one green marble. You draw one marble. Write the sample space and assign probabilities so they sum to 1.
Example 13
mediumA spinner has 3 sections: Red (probability 0.5), Blue (probability 0.3), and Green. Find and verify the sample space probabilities sum to 1.
Example 14
hardA die is rolled. What is the size of the event 'rolling a prime number'?
Example 15
mediumList the sample space for flipping three coins.
Example 16
mediumA bag has 3 red, 2 blue. How many ways to draw 2 without regard to order?
Example 17
mediumHow many outcomes for the ordered pair of two dice summing to 5?
Example 18
hardA code consists of digits from –. How many outcomes are in the sample space if digits may repeat?
Example 19
easyA drawer has shirts of different colors. You pick one. How many outcomes are in the sample space?
Example 20
hardTwo dice are rolled. What is the size of the event 'both dice show the same number'?