# Browsing category probability

## A coin sequence conundrum

Zeke and Monty play a game. They repeatedly toss a coin until either the sequence tail-tail-head (TTH) or the sequence tail-head-head (THH) appears. If TTH shows up first, Zeke wins; if THH shows up first, Monty wins. What is the probability that Zeke wins? My first reaction to this question

## An ex-Formula 1 driver asks… why does nobody ever ask me my opinion?

Former Formula 1 driver @MBrundleF1 asks: These election opinion polls. I've never been approached, nor has anybody I know, about a poll on anything whatsoever. Who are these people? — Martin Brundle (@MBrundleF1) April 5, 2015 (Obviously, he didn't ask me specifically, but I thought it was a good question.)

## Leave poor Hannah alone!

Gosh, who would have thought it? 15,000 students (at the time of writing) have signed a petition to get EdExcel to change the grade boundaries for Thursday's non-calculator GCSE paper. Good luck with that. The boundaries will have been set using magic statistics, and either have been or will be

## The Mathematical Ninja takes on the Wall Game

For the first time anyone could remember, the Mathematical Ninja trembled with fear. He’d pulled his scary face, and it hadn’t worked: Victoria Coren Mitchell had simply said “you don’t scare me” and he had no idea what to do next. “It’s time for the wall game,” she said. “Right,”

## Probability and prediction

A reader asks: Is it easier to predict every game in the first round of a tournament1, or to pick the eventual winner? There's a competition run by Sky, which is free to enter; you win £250,000 if you correctly predict the scores in six Premier League games. It's free

## What percentage of numbers have a seven in?

Someone on the internet asks: What percentage of the natural numbers have the digit 'seven' in them? This is going to sound like a weird answer: it's 100%. I know, I know: you can point at 42 and 100 and 986,543,210 and 666,666,666,666,666 and at least a handful of others

## Sam Warburton’s Dilemma

There are six minutes to play in the last Autumn international, and Australia are leading Wales by 30 points to 26. Australia, however, have just conceded a penalty in front of the posts, leaving the Welsh captain, Sam Warburton, with a dilemma: should he kick at goal (and take a

## Why you don’t add across probability trees – Secrets of the Mathematical Ninja

"... Evidently not," said the student, with a look of sheer terror that was music to the Mathematical Ninja's eyes. He smiled a nasty smile. "No," he said, "you categorically do not add probabilities as you go through the tree." "You... multiply?" The student was cautious. The Mathematical Ninja hadn't

## The Bayesian umbrella

At a recent MathsJam, there was a puzzle. This is nothing out of the ordinary. It went something like: If an absent-minded professor takes his umbrella into a classroom, there's a probability of $\frac{1}{4}$ that he'll absent-mindedly leave it there. One day, he sets off with his umbrella, teaches in

## How related are Alice and Bob?

The population of Iceland is somewhere around 300,000. It's not an incredibly big island, and there's not a huge amount of immigration and emigration - which means, if you're on the Icelandic dating scene, you have to be fairly careful not to go out with uncomfortably close relatives. Luckily, there's