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Sample space for coin toss

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

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Student-friendly explanation

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.

How to write this in exams

  1. 1

    Start with the exact idea

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

  2. 2

    Then show how to use it

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

  3. 3

    Add one concrete example

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

  4. 4

    Avoid this incomplete answer

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

Definition

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

Example

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

Rule to remember

For one coin toss, S = {H, T}. For two coin tosses, S = {HH, HT, TH, TT}.

Memory hook

One toss, two outcomes; two tosses, four ordered outcomes.

Examples and method

Worked example

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

Method to apply

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

Diagram support

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

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.

Avoid common mistakes

Common confusion

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

Common wrong answer

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

Exam tip

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

Quick check

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

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

Answer writing and exam use

1-mark answer

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

2-mark answer

The sample space for a coin toss is the set of all possible outcomes of that toss. For one coin toss, S = {H, T}. For two coin tosses, S = {HH, HT, TH, TT}. For two coin tosses, the sample space is {HH, HT, TH, TT}.

3-mark answer

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. For one coin toss, S = {H, T}. For two coin tosses, S = {HH, HT, TH, TT}. If two coins are tossed, the complete sample space has 4 outcomes. So the number of possible outcomes is 4, not 3, because HT and TH are different. Questions usually ask students to list the sample space or count the total number of outcomes for one or more tosses. A common wrong answer is {HH, HT, TT} because the student forgets that TH is also a different outcome.
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