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Coin Tossing Games

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?

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Fixing the Odds

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?

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Penta Colour

In how many different ways can I colour the five edges of a pentagon red, blue and green so that no two adjacent edges are the same colour?

The Birthday Bet

Age 14 to 16 Challenge Level:
What is the chance that one person's birthday is different from that of another person chosen at random ?

So what is the chance that their birthdays do match ?

Given that the first two did not match, what is the chance that a third person will not match with either of those first two ?

Can you now calculate the probability that all three birthdays are different ?