More Life Probabilities

The probability of someone driving at or below the speed limit is less than half. According to Arizona data from 2002, the probability that someone is traveling below a 55-mph speed limit is 28%, and 43% in a 65-mph speed zone. It increases at 75 mph to 51%. Assuming this is typical of other areas, we can make some predictions.

What's the likelihood that one of the 10 cars in front of you is going at or below the speed limit, and will slow you down? The answer will be the complement to the probability of exceeding the speed limit to the tenth power, or the probability that all 10 cars will be going faster than the speed limit: p(0)=0.72^10 for a 55-mph speed zone, or 3.7%. You have a 96% chance of slowing down if you are going faster than the speed limit. The probability of slowing down increases as more cars are in front of you. Maybe that's why so many people pass me to get to the traffic jam first.

You do a little better if there's two lanes. Your chance of slowing down decreases to 93%. Whoopee!

Your chance of winning the big payout in a micro-lottery of twelve numbers is 1 in 924. Unless the payout is more than $1,000, don't participate.

And you may not want to participate in issuing credit cards. It's often reported that an average household has over $7,000 in credit card debt. Others have done more analysis on this number to show that it's misleading. Before you think about issuing your own credit card to your customers to capture some interest income, think about these facts: 27% of the households in 2010 didn't have a credit card; 61% pay off their charges each month not incurring any interest; the median level of credit card debt is $2,600 in 2010. Taking some of the initial data into account, some have said that the average debt is over $15,000 per household. If that's so, and the median is only $2,600 then there must be a very long distribution tail with some very high credit card balances to pull the average so far above the median.

Suppose interest rates follow a normal distribution and average 16%, what can you expect to earn on the cards you issue? Perhaps the best estimate is $162/yr for every card issued (39% x $2600 x 16%). Is it worth it to create a whole business system to administer this--signing up customers and reporting to credit agencies, etc.? You decide. Don't overestimate the potential income. Quite a few years ago, the head of the AT&T credit card department was fired for not hitting income projections. They forgot to account for most people paying off the balances every month.