Combining probabilities

  • Snooker Frames
    problem

    Snooker frames

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

    It is believed that weaker snooker players have a better chance of winning matches over eleven frames (i.e. first to win 6 frames) than they do over fifteen frames. Is this true?

  • Dicey Decisions
    problem

    Dicey decisions

    Age
    16 to 18
    Challenge level
    filled star empty star empty star
    Can you devise a fair scoring system when dice land edge-up or corner-up?
  • Put Out
    problem

    Put out

    Age
    16 to 18
    Challenge level
    filled star filled star filled star

    After transferring balls back and forth between two bags the probability of selecting a green ball from bag 2 is 3/5. How many green balls were in bag 2 at the outset?