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Comparing likelihood of events

Comparing likelihood means deciding which event is more likely by comparing their probabilities.

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Student-friendly explanation

If one event has a larger probability than another, it is more likely to happen. This skill is important in exam questions that ask students to compare two choices, two bags, or two spinners. The student must compare the fractions carefully, not just look at the numbers in the numerator or denominator alone.

How to write this in exams

  1. 1

    Start with the exact idea

    Comparing likelihood means deciding which event is more likely by comparing their probabilities.

  2. 2

    Then show how to use it

    1. Find each probability. 2. Simplify the fractions. 3. Compare them using a common denominator if needed. 4. Choose the larger probability.

  3. 3

    Add one concrete example

    An event with probability 3/5 is more likely than an event with probability 1/4.

  4. 4

    Avoid this incomplete answer

    A common wrong answer is choosing 3/8 over 1/2 because 3 looks larger than 1, even though the denominators matter too.

Definition

Comparing likelihood means deciding which event is more likely by comparing their probabilities.

Example

An event with probability 3/5 is more likely than an event with probability 1/4.

Rule to remember

A larger probability means a more likely event; compare the values after simplifying if needed.

Memory hook

Bigger probability means better chance.

Examples and method

Worked example

Event A has probability 3/8 and Event B has probability 1/2. Since 1/2 = 4/8, Event B is more likely than Event A.

Method to apply

1. Find each probability. 2. Simplify the fractions. 3. Compare them using a common denominator if needed. 4. Choose the larger probability.

Diagram support

A simple number line from 0 to 1 can help compare event probabilities quickly.

How CBSE asks it

Students may be asked to choose the more likely event among two experiments, spinners, or bags.

Avoid common mistakes

Common confusion

Students sometimes compare only the denominators or only the numerators and ignore the full fraction.

Common wrong answer

A common wrong answer is choosing 3/8 over 1/2 because 3 looks larger than 1, even though the denominators matter too.

Exam tip

Convert probabilities to the same form before deciding which event is more likely.

Quick check

Which is more likely: an event with probability 2/3 or an event with probability 3/5?

The event with probability 2/3 is more likely because 2/3 is greater than 3/5 when compared as fractions.

Answer writing and exam use

1-mark answer

Comparing likelihood means deciding which event is more likely by comparing their probabilities.

2-mark answer

Comparing likelihood means deciding which event is more likely by comparing their probabilities. A larger probability means a more likely event; compare the values after simplifying if needed. An event with probability 3/5 is more likely than an event with probability 1/4.

3-mark answer

If one event has a larger probability than another, it is more likely to happen. This skill is important in exam questions that ask students to compare two choices, two bags, or two spinners. The student must compare the fractions carefully, not just look at the numbers in the numerator or denominator alone. A larger probability means a more likely event; compare the values after simplifying if needed. Event A has probability 3/8 and Event B has probability 1/2. Since 1/2 = 4/8, Event B is more likely than Event A. Students may be asked to choose the more likely event among two experiments, spinners, or bags. A common wrong answer is choosing 3/8 over 1/2 because 3 looks larger than 1, even though the denominators matter too.
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