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medium difficulty5 min

Comparing likelihood of events

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

In one line: Bigger probability means better chance.

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Understand it

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.

Formula and rule

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

See it worked out

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

Worked example

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

Method you can reuse

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

Visual tip

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

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

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

Think first, then show answer
The event with probability 2/3 is more likely because 2/3 is greater than 3/5 when compared as fractions.

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.

Don't mix this up

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

Exam tip

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

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

Students may be asked to choose the more likely event among two experiments, spinners, or bags.
  1. 1

    Enough for 1 mark

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

  2. 2

    Add for 2 marks

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

  3. 3

    Add for 3 marks

    Event A has probability 3/8 and Event B has probability 1/2.

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