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Gambling at Monte Carlo

A man went to Monte Carlo to try and make his fortune. Whilst he was there he had an opportunity to bet on the outcome of rolling dice. He was offered the same odds for each of the following outcomes: At least 1 six with 6 dice. At least 2 sixes with 12 dice. At least 3 sixes with 18 dice.

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Balls and Bags

Two bags contain different numbers of red and blue balls. A ball is removed from one of the bags. The ball is blue. What is the probability that it was removed from bag A?

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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?

The Better Bet

Stage: 4 Challenge Level: Challenge Level:1
No matter how big the prize or how easy it looks to win, it isn't smart to bet if we can't stand the loss.

However, lots of things are not certain and we often need to make decisions in the face of that uncertainty.

Probability is how mathematicians quantify uncertainty, and games are an excellent way to explore this.

So which of the following is the better bet, if both games cost $£1$ to play?

Getting two heads and two tails on four coins wins you $£3$.

or

You get $£2$ for every six that appears when three standard dice are rolled.

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