Theoretical probability

problem
Snooker frames

Age

16 to 18

Challenge level

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?
problem
Teams

Age

16 to 18

Challenge level

Two brothers belong to a club with 10 members. Four are selected for a match. Find the probability that both brothers are selected.
problem
How many balls?

Age

16 to 18

Challenge level

A bag contains red and blue balls. You are told the probabilities of drawing certain combinations of balls. Find how many red and how many blue balls there are in the bag.
problem
Stats statements

Age

16 to 18

Challenge level

Are these statistical statements sometimes, always or never true? Or it is impossible to say?
problem
Succession in Randomia

Age

16 to 18

Challenge level

By tossing a coin one of three princes is chosen to be the next King of Randomia. Does each prince have an equal chance of taking the throne?
problem
Rain or shine

Age

16 to 18

Challenge level

Predict future weather using the probability that tomorrow is wet given today is wet and the probability that tomorrow is wet given that today is dry.
problem
Put out

Age

16 to 18

Challenge level

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?
problem
The Derren Brown coin flipping scam

Age

16 to 18

Challenge level

Calculate probabilities associated with the Derren Brown coin scam in which he flipped 10 heads in a row.