Combining probabilities

  • Molecular sequencer
    problem

    Molecular Sequencer

    Age
    14 to 18
    Challenge level
    filled star filled star empty star
    Investigate the molecular masses in this sequence of molecules and deduce which molecule has been analysed in the mass spectrometer.
  • Squash
    problem

    Squash

    Age
    16 to 18
    Challenge level
    filled star filled star filled star
    If the score is 8-8 do I have more chance of winning if the winner is the first to reach 9 points or the first to reach 10 points?
  • How Risky \is my diet?
    problem

    How Risky Is My Diet?

    Age
    11 to 16
    Challenge level
    filled star filled star empty star

    Newspapers said that eating a bacon sandwich every day raises the risk of bowel cancer by 20%. Should you be concerned?

  • Statins and Risk
    problem

    Statins and Risk

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    "Statins cut the risks of heart attacks and strokes by 40%"
    Should the Professor take statins? Can you help him decide?

  • Handling Data - Short Problems
    problem

    Odd Dice

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

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

  • Fabric bag open at the top, showing a number of blue marbles.
    problem

    Marbles and Bags

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    Two bags contain different numbers of red and blue marbles. A marble is removed from one of the bags. The marble is blue. What is the probability that it was removed from bag A?

  • Gambling at Monte Carlo
    problem

    Gambling at Monte Carlo

    Age
    14 to 16
    Challenge level
    filled star filled star filled star

    A man went to Monte Carlo to try and make his fortune. Is his strategy a winning one?

  • Fixing the Odds
    problem

    Fixing the Odds

    Age
    14 to 16
    Challenge level
    filled star filled star filled star

    You have two bags, four red balls and four white balls. You must put all the balls in the bags although you are allowed to have one bag empty. How should you distribute the balls between the two bags so as to make the probability of choosing a red ball as small as possible and what will the probability be in that case?

  • Voting Paradox
    problem

    Voting Paradox

    Age
    14 to 18
    Challenge level
    filled star filled star empty star

    Some relationships are transitive, such as 'if A>B and B>C then it follows that A>C', but some are not. In a voting system, if A beats B and B beats C should we expect A to beat C?