Conditional probability

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
The birthday bet

Age

14 to 16

Challenge level

The next ten people coming into a store will be asked their birthday. If the prize is £20, would you bet £1 that two of these ten people will have the same birthday ?
problem
Two's company

Age

11 to 14

Challenge level

Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?
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
In a box

Age

14 to 16

Challenge level

Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?
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?
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?
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?
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?
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?