This is part of our collection of Short Problems.

You may also be interested in our longer problems on Probability - Stage 4.

Printable worksheets containing selections of these problems are available here

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### Tying the Rope

What is the probability that two pieces of rope are tied together, when Pat ties two loose ends together?

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### Collecting Marbles

How many marbles need to be taken out to ensure that at least three are of the same colour?

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### Swapping Sweets

If two girls each take a sweet from each other's bags, what is the probability that they end up with what they started with?

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### Flipping coins

A coin is flipped 4 times. What is the probability of getting heads at least 3 times?

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### Odd Dice

These strange dice are rolled. What is the probability that the sum obtained is an odd number?

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### One or both

Problem 1 was solved by 70% of the pupils. Problem 2 was solved by 60% of them. Can you work out how many pupils took the exam?

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### Takeaway Time

Pizza, Indian or Chinese takeaway? If everyone liked at least one, how many only liked Indian?

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### Switch On

In how many different ways can a row of five "on/off" switches be set so that no two adjacent switches are in the "off" position?

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### XOXOXO

6 tiles are placed in a row. What is the probability that no two adjacent tiles have the same letter on them?

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### Different Digital Clock

At how many times between 10 and 11 o'clock are all six digits on a digital clock different?

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### Medal Ceremony

The teacher has forgotten which pupil won which medal. In how many different ways could he give the medals out to the pupils?

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### Descending Deal

Four cards from a set numbered 1-36 are dealt. What is the probability that they are dealt in order?

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### Two Girls

There are 10 girls in a mixed class. If two pupils are selected, the probability that they are both girls is 0.15. How many boys are in the class?

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### Phone Call

How many different phone numbers are there starting with a 3 and with at most two different digits?

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### Vegtown Elections

What percentage of people voted for the Broccoli party in the Vegtown election?

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### Domino Match

If you take two dominoes from a set at random, what is the probability that they 'match'?