Monday puzzle: who will toss more heads?
Let's you and I play a game with coins. You have 100 dimes, and I have 99 pennies. At the same time, we will toss our coins in the air and let them fall on the floor. Then we meticulously count the outcomes of our tosses. You win if you show more ...

Monday puzzle: which lane is better?
You're on a two-lane highway and there are cars ahead of you in both lanes. You want to go straight ahead, but some of the cars in front of you might slow down to turn and delay you. You are in the left lane. In that lane, there are 3 cars, ...

Why Skydiving is not safer than driving
I had a hard time accepting that skydiving could ever be considered a low-risk activity. Call me old fashioned, but it just doesn't seem prudent to be jumping out of an airplane with a parachute as your life support. But however I feel personally doesn't really matter. I'm happy to judge ...

Monday puzzle: Excel random numbers
The Excel function rand() generates a random number between 0 and 1. Let's say I generate two numbers using the rand() function. What is the probability the two numbers sum is less than 1 AND their product is less than 3/16? Give it a try, or experiment numerically, before reading the answer after ...

The three coin puzzle
After a lucky day in the casino, a gambler is greeted by a beautiful woman in the hotel lobby. She congratulates the gambler on his success, and wonders if he would like to parlay those winnings into even more money. She offers the following bet:

Allais Paradox: how low probability events deceive us
This is a fun example in decision theory that demonstrates how are preferences can be inconsistent. As a point of trivia, Maurice Allais won the Nobel Prize for other research, but he is most remembered today for this paradox. (h/t: Falkenblog). The paradox is best illustrated with a brief experiment that I'll ...

Monday puzzle: random music
Have you ever felt your iPod or music player's shuffle function was not working correctly? Today's problem is about how random events are not always perceived as random.

What’s the probability of a pure strategy Nash equilibrium?
This is a problem I adapted from the free e-book Algorithmic Game Theory. I had some fun solving it, and so I wanted to share it.

Puzzle: birthday line problem
Birthday problems always make for fun probability puzzlers. There's the famous birthday problem, and then there is one I wrote about before called birthday holidays. The following is a puzzle I have adapted from the website braingle.

Monday puzzle: flip until heads
Probability calculations often show counter-intuitive results. Here is a puzzle about the distribution of coin flips.

The card game le her
While game theory as we know it began about 60 years ago, there were game theory ideas dating back to hundreds and thousands of years ago (see how game theory solved a religious mystery). Another early example happened in 1713, when James Waldegrave provided a mixed strategy solution to a two-person ...

Monday puzzle: lady tasting tea problem
In a previous post, I discussed ways to design a better blind taste test. This puzzle is about a taste test with historic significance to statistics.

Puzzle: random size confetti
Today's puzzle is about statistical sampling, adapted from a problem I found in this book. Professor X teaches a probability class. He assigns a holiday-themed project to his students.

Puzzle: a Christmas probability
This year Christmas will fall on a Sunday, but last year Christmas happened on a Saturday, and in general, the day can change from year to year. Because of the way dates rotate, you might think that Christmas can fall on every day of the week with equal probability. But in ...

Puzzle: odds of a comeback victory
You're favorite sports team is down at halftime, but you are hoping they can pull it together and eek out a victory. What are the odds of that happening? The probability obviously depends on the exact game in question. But I came across an interesting probability problem that gives an interesting ...