Probability

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

    Penta Colour

    Age
    14 to 16
    Challenge level
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    In how many different ways can I colour the five edges of a pentagon so that no two adjacent edges are the same colour?

  • 396
    problem

    396

    Age
    14 to 16
    Challenge level
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    The four digits 5, 6, 7 and 8 are put at random in the spaces of the number : 3 _ 1 _ 4 _ 0 _ 9 2 Calculate the probability that the answer will be a multiple of 396.

  • Tying the Rope
    problem

    Tying the Rope

    Age
    14 to 16
    Challenge level
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    What is the probability that two pieces of rope are tied together, when Pat ties two loose ends together?

  • Handling Data - Short Problems
    problem

    Boy or Girl?

    Age
    14 to 16
    Challenge level
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    Will the witch make a profit or loss?

  • Statins and Risk
    problem

    Statins and Risk

    Age
    14 to 16
    Challenge level
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    "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
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    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
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    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?

  • Coin Tossing Games
    problem

    Coin Tossing Games

    Age
    14 to 16
    Challenge level
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    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?

  • Win or Lose?
    problem

    Win or Lose?

    Age
    14 to 16
    Challenge level
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    A gambler bets half the money in his pocket on the toss of a coin, winning an equal amount for a head and losing his money if the result is a tail. After 2n plays he has won exactly n times. Has he more money than he started with?

  • Thank your Lucky Stars
    problem

    Thank Your Lucky Stars

    Age
    14 to 16
    Challenge level
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    A counter is placed in the bottom right hand corner of a grid. You toss a coin and move the star according to the following rules: ... What is the probability that you end up in the top left-hand corner of the grid?