Practice Sample Space in Statistics
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
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.
Example 1
easyList the sample space for rolling a standard six-sided die and flipping a coin simultaneously.
Example 2
mediumA restaurant offers 3 starters (soup, salad, bread), 4 mains (chicken, fish, beef, pasta), and 2 desserts (cake, fruit). How many different 3-course meals are possible? Do you need to list them all?
Example 3
mediumA password consists of one letter (A–E) followed by one digit (1–3). (a) List the entire sample space. (b) How many passwords contain the letter 'C'? (c) What is the probability of randomly generating a password that starts with 'C'?
Example 4
hardTwo 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?