Understanding of statistics and probability is one of the most undervalued skills. Obviously in business, but equally in your private life. Why? Well, firstly it can help you to ask the right question, and then secondly answer them.
Einstein is (incorrectly) credited for having said: “If I had an hour to solve a problem I’d spend 55 minutes thinking about the problem and five minutes thinking about solutions.” In other words, there is more value in understanding the problem, asking the right questions, than in having a solution – and in many situations we think we understand the problem (or question) and jump straight into answering it.
Meeting someone on vacation
You will often hear people returning from vacation saying “what are the odds of (randomly) meeting Madeleine and Bob in Spain during the Paella festival”? And those odds are actually very high. Location, point in time and the exact people you need to meet. A lot of things need to be true, and that makes it virtually impossible, which turns it into a fantastic dinner party story.
However, the question actually doesn’t address the real probability, because the right question is, “what are the odds of meeting someone I know at some point during my vacation?” – and we could actually extend that to “any vacation”, because at a dinner party who actually cares, which specific vacation it was?
Those odds are significantly lower. You know people, likely in the same income range as yourself, located in the same town, with same vacation preferences etc. In a worst case scenario, BBC calculated that the chances of meeting your boss on vacation is 1 to 1.000. If you know 299 other people by first name, then there is actually a 30% chance of meeting somebody you know on vacation…
Winning the lottery – twice!
Likewise Evelyn Adams won the New Jersey lottery twice in 1985 and 1986. The odds were 1 to 3.2 million and 1 to 5.2 million respectively. So the odds of a specific person winning those specific lotteries were 1 to 16,6 trillion. However, if you reverse the question and ask “what are the odds of SOMEONE winning the lottery twice any time in a seven year period?”, the answer is a surprising 50:50 chance as calculated by Byron Jones and Robb Muirhead. That angle on the story gets far less clicks…
Same – or different questions?
It is just one of those days. You are in need of a haircut and a new car.
In your local town you can get you hair cut for $150, but you can go to the next town 20 minutes away, and get it cut for $80. Assuming it is of similar quality (it never is…I know) etc., which do you choose?
In your local town a brand new Toyota Supra costs $56,180. In the next town, you can get it for $56,110. Which do you choose?
If you disregard the need to support your local shops, you might know someone who works there etc. most people would probably answer “next town – it is almost twice as expensive here” to the haircut and “here – there is virtually no difference in the price” to the car.
However, the question being asked is actually: “Are you willing to spend time, and transport costs, to go to the next town to save $70?” – and what if you had already decided to get the haircut there, would you still go back home to buy the car?
The last example obviously had very little to do with probability and statistics, but purely based on economics. However, they may be slightly fat fetched, but they all highlight that we are all likely to make assumptions about understanding the situation, and not truly understanding the actual question. Less because of ignorance – and mostly because we are humans.