Skip over navigation
Cambridge University Faculty of Mathematics NRich logo
menu search
  • Teachers expand_more
    • Early years
    • Primary
    • Secondary
    • Post-16
    • Events
    • Professional development
  • Students expand_more
    • Primary
    • Secondary
    • Post-16
  • Parents expand_more
    • Early Years
    • Primary
    • Secondary
    • Post-16
  • Problem-Solving Schools
  • About NRICH expand_more
    • About us
    • Impact stories
    • Support us
    • Our funders
    • Contact us
  • search

Or search by topic

Number and algebra

  • The Number System and Place Value
  • Calculations and Numerical Methods
  • Fractions, Decimals, Percentages, Ratio and Proportion
  • Properties of Numbers
  • Patterns, Sequences and Structure
  • Algebraic expressions, equations and formulae
  • Coordinates, Functions and Graphs

Geometry and measure

  • Angles, Polygons, and Geometrical Proof
  • 3D Geometry, Shape and Space
  • Measuring and calculating with units
  • Transformations and constructions
  • Pythagoras and Trigonometry
  • Vectors and Matrices

Probability and statistics

  • Handling, Processing and Representing Data
  • Probability

Working mathematically

  • Thinking mathematically
  • Developing positive attitudes
  • Cross-curricular contexts

Advanced mathematics

  • Decision Mathematics and Combinatorics
  • Advanced Probability and Statistics
  • Mechanics
  • Calculus

For younger learners

  • Early Years Foundation Stage

Do Rare Events Happen?

Age 11 to 16
Challenge Level Yellow starYellow star
  • Problem
  • Student Solutions

This resource is part of the collection Probability and Evidence.



Do you think there is a family in the UK with three children who all have the same birthday (but born in different years)?

How rare do you think this is?

How often do you think a baby is born in the UK who shares their birthday with both their older siblings? Do you think it happens:
  • To several families per year?
  • To one family per year?
  • Only every few years?
  • Less often?


Can you calculate the probability that this might happen to a particular family?

When you've thought about this question, click on the button below:


A child is born. Later on, some siblings are born...

What is the probability that the second child is born on the same day as the first child?

What is the probability that the third child is born on the same day as the first child?

Can you combine these probabilities to find the probability that all three children are born on the same day?
 


What assumptions have you made in these calculations? Do you think these assumptions are reasonable?



If there are 1 million families in the UK with at least three children, how many of these would you expect to have three children born on the same day?

How does this compare with your original thoughts?


You can read more about the probabilities on Plus or Understanding Uncertainty, and you might like to try Last One Standing.
  • Tech help
  • Accessibility Statement
  • Sign up to our newsletter
  • Twitter X logo

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

University of Cambridge logo NRICH logo