The set of all possible outcomes in an experiment is called the sample space. The sample space may be listed within brackets, separated by commas as shown below.
- (i) Experiment: A coin is tossed
- (ii) Experiment: A die is rolled
Step-by-step solution
Idea: To write a sample space, list every outcome that can happen, each one once, inside curly brackets { } separated by commas.
(i) Experiment: A coin is tossed
- A coin has two faces. It can land showing Heads (H) or Tails (T). Nothing else can happen (we ignore the coin landing on its edge).½ mark
- Sample space: {H, T}. It has 2 outcomes.½ mark
(ii) Experiment: A die is rolled
- A die has 6 faces with 1, 2, 3, 4, 5 and 6 dots. The outcome is the number of dots on the top side when it stops.½ mark
- Sample space: {1, 2, 3, 4, 5, 6}. It has 6 outcomes.½ mark
Check: Every possible result appears once, and nothing impossible (like 0 or 7 on a die) is listed.
Answer to write in the exam
(i)
Possible outcomes: Heads (H) or Tails (T)
∴ Sample space = {H, T}
(ii)
Possible outcomes: top side shows 1, 2, 3, 4, 5 or 6 dots
∴ Sample space = {1, 2, 3, 4, 5, 6}
Common mistakes that cost marks
- Writing the sample space of a die as {6}, or as {1, 6}. It must list all six possible outcomes.
- Listing an outcome twice, e.g. {H, T, H}. Each outcome is written only once.
- Using round brackets ( ) instead of curly brackets { } for the set.
How this can come in the exam
A spinner has three equal sectors coloured red, green and yellow. The sample space for one spin is
- {red}
- {red, green}
- {red, green, yellow}
- {1, 2, 3, 4}
Show answer
(C) {red, green, yellow}
The arrow can stop on any of the three colours, so all three must be listed: {red, green, yellow}.
Write the sample space when (a) a card is picked from four cards marked A, B, C, D; (b) a day of the week is chosen at random. How many outcomes does each have?
Show answer
(a) {A, B, C, D}: 4 outcomes. (b) {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}: 7 outcomes.Try one yourself
Write the sample space for choosing one letter at random from the word MATH.
Show answer
{M, A, T, H}: 4 outcomes.
More questions like this
- Suppose you roll a die 50 times, and it lands on a 4 exactly 8 times.
- If you roll a standard 6-sided die, what is the theoretical probability of getting a 4?
- A letter is picked at random from the word ‘PROBABILITY’. What is the probability of picking the letter B?
- Suppose you anonymously collect information regarding the favourite fruit of 50 students in your class. Let us assume that the results are: 20 students like mango, 15 students like apples, 10 students like bananas, and 5 students like grapes. Let us play a game! Suppose we randomly pick one student from the class and try to guess their favourite fruit. What’s the probability that the student’s favourite fruit is mango?
- If I have rolled a 4 on a die 8 times in succession, the probability of rolling a 4 again is still only ≈ 0.16 (assuming the die is fair). Probability does not tell you what will happen next but predicts what will happen in the long run.