medium difficulty7 min

Probability in spinner or bag contexts

This is probability applied to a spinner or a bag where each sector or item may represent an outcome.

In one line: Count the marked parts, then divide by all equal parts.

Understand it

In spinner questions, equal sectors mean equal chance. In bag questions, the count of each colour or type decides the probability. These problems are common because they connect direct counting with a visual model that students can understand quickly.

Example

If a spinner has 5 equal parts and 2 are blue, the probability of blue is 2/5.

Formula and rule

Probability = favourable parts or items / total equal parts or total items.

See it worked out

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

Worked example

A spinner has 8 equal sectors, 3 of which are red.

1Probability of red = 3/8.
2Equal sector size is the key reason this works.

Method you can reuse

1Check the model: spinner or bag.
2Count favourable sectors or items.
3Count total sectors or items.
4Divide and simplify.

Sketch it in your answer

Use a coloured sector sketch for a spinner or a count table for a bag.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

A bag has 4 yellow marbles and 6 green marbles. What is the probability of drawing a yellow marble?

Think first, then show answer

There are 10 marbles in total and 4 are yellow, so the probability is 4/10, which simplifies to 2/5.

Common wrong answer

A common wrong answer is counting only the favourable sectors and forgetting the total number of equal sectors.

Don't mix this up

Students sometimes count colours or sectors without checking whether they are equal in size.

Exam tip

For spinners, check equal parts. For bags, count the exact number of items of each type.

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 show a spinner, a coloured disc, or a bag of objects and ask for the probability of a colour or symbol.

1
Enough for 1 mark
This is probability applied to a spinner or a bag where each sector or item may represent an outcome.
2
Add for 2 marks
Example: If a spinner has 5 equal parts and 2 are blue, the probability of blue is 2/5.
3
Add for 3 marks
A spinner has 8 equal sectors, 3 of which are red.

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