Conditional probability

  • Squash
    problem

    Squash

    Age
    16 to 18
    Challenge level
    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?
  • Master Minding
    problem

    Master Minding

    Age
    11 to 14
    Challenge level

    Your partner chooses two beads and places them side by side behind a screen. What is the minimum number of guesses you would need to be sure of guessing the two beads and their positions?

  • How Risky \is my diet?
    problem

    How Risky Is My Diet?

    Age
    11 to 16
    Challenge level

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

  • Five coloured cubes forming the edges of a pentagon.
    problem

    Penta Colour

    Age
    14 to 16
    Challenge level

    In how many different ways can I colour the five edges of a pentagon so that no two adjacent edges are the same colour?

  • Statins and Risk
    problem

    Statins and Risk

    Age
    14 to 16
    Challenge level

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

  • Coin Tossing Games
    problem

    Coin Tossing Games

    Age
    14 to 16
    Challenge level

    You and I play a game involving successive throws of a fair coin. Suppose I pick HH and you pick TH. The coin is thrown repeatedly until we see either two heads in a row (I win) or a tail followed by a head (you win). What is the probability that you win?

  • Small tomato seedlings in yellow pots.
    problem

    Winning Marble

    Age
    14 to 16
    Challenge level

    How can this prisoner escape?

  • Fixing the Odds
    problem

    Fixing the Odds

    Age
    14 to 16
    Challenge level

    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?

  • Small tomato seedlings in yellow pots.
    problem

    Dropouts

    Age
    14 to 16
    Challenge level

    What percentage of students who graduate have never been to France?

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