Conditional probability

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

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?
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?
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

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?
problem

Winning Marble

Age

14 to 16

Challenge level

How can this prisoner escape?
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

Dropouts

Age

14 to 16

Challenge level

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

Do You Brush Your Teeth Every Day?

Age

14 to 18

Challenge level

How can we find out answers to questions like this if people often lie?