Combining probabilities

problem
Favourite

Knock-Out

Age

16 to 18

Challenge level

Before a knockout tournament with 2^n players I pick two players. What is the probability that they have to play against each other at some point in the tournament?
problem
Favourite

At Least One...

Age

11 to 14

Challenge level

Imagine flipping a coin a number of times. Can you work out the probability you will get a head on at least one of the flips?
problem
Favourite

The Better Choice

Age

14 to 16

Challenge level

Here are two games you can play. Which offers the better chance of winning?
problem
Favourite

Same Number!

Age

14 to 16

Challenge level

If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?
problem
Favourite

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
Favourite

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

Chance Combinations

Age

11 to 14

Challenge level

Can you design a bingo board that gives you the best chance of winning?
$How Risky \is my diet?$

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

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

Win or Lose?

Age

14 to 16

Challenge level

A gambler bets half the money in his pocket on the toss of a coin, winning an equal amount for a head and losing his money if the result is a tail. After 2n plays he has won exactly n times. Has he more money than he started with?