Combining probabilities

Can you design a bingo board that gives you the best chance of winning?

Newspapers said that eating a bacon sandwich every day raises the risk of bowel cancer by 20%. Should you be concerned?

"Statins cut the risks of heart attacks and strokes by 40%"
Should the Professor take statins? Can you help him decide?

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?

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?

Some relationships are transitive, such as `if A>B and B>C then it follows that A>C', but some are not. In a voting system, if A beats B and B beats C should we expect A to beat C?

This article, for students and teachers, is mainly about probability, the mathematical way of looking at random chance and is a shorter version of Taking Chances Extended.

Explore the distribution of molecular masses for various hydrocarbons

Investigate the molecular masses in this sequence of molecules and deduce which molecule has been analysed in the mass spectrometer.