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medium difficulty5 min

Sample space for coin toss

The sample space for a coin toss is the set of all possible outcomes of that toss.

In one line: One toss, two outcomes; two tosses, four ordered outcomes.

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Understand it

For one toss of a fair coin, the sample space is {H, T}. For two coin tosses, order matters, so the sample space has four outcomes: HH, HT, TH, and TT. Writing the full sample space is the first step before finding probability.

Example

For two coin tosses, the sample space is {HH, HT, TH, TT}.

Formula and rule

For one coin toss, S = {H, T}.

For two coin tosses, S = {HH, HT, TH, TT}.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

  1. 1If two coins are tossed, the complete sample space has 4 outcomes.
  2. 2So the number of possible outcomes is 4, not 3, because HT and TH are different.

Method you can reuse

  1. 1Decide how many tosses are made.
  2. 2Write the possible outcome for each toss.
  3. 3Combine them in order.
  4. 4List all distinct outcomes without skipping any.

Visual tip

A two-level tree diagram helps list all outcomes of two coin tosses clearly.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

What is the sample space when a coin is tossed twice?

Think first, then show answer
The sample space is {HH, HT, TH, TT}, because each toss can be H or T and the order of the two tosses matters.

Common wrong answer

A common wrong answer is {HH, HT, TT} because the student forgets that TH is also a different outcome.

Don't mix this up

Students often miss ordered outcomes like HT and TH and write only three outcomes.

Exam tip

When more than one coin is tossed, write outcomes in order so you do not miss any case.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Questions usually ask students to list the sample space or count the total number of outcomes for one or more tosses.
  1. 1

    Enough for 1 mark

    The sample space for a coin toss is the set of all possible outcomes of that toss.

  2. 2

    Add for 2 marks

    Example: For two coin tosses, the sample space is {HH, HT, TH, TT}.

  3. 3

    Add for 3 marks

    Writing the full sample space is the first step before finding probability.

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