# 50/50

50/50?

What happens when someone digs without first calling 811 to get an underground utility locate?   Well, there are two possible outcomes.

You hit something.

You don’t hit something.

Vegas odds makers would call that the proverbial 50/50 chance.

But is it really, truly, actually 50/50?

Here’s a well thought-out item from www.thecalculatorsite.com

It’s obvious that the chances of a normal two-sided coin coming down heads, rather than tails, are exactly 50/50 for each throw. The coin can only land on one side or the other (event) but there are two possible outcomes: heads or tails. One over two is a half, or 50 per cent. What’s not so obvious is that the probability of a coin that has come up heads for the past 19 flips also landing heads up on the 20th throw is also 50 per cent.

You might object that such an event would be most unlikely – and you’d be right. Nevertheless, looked at logically, you can see that the ‘unprecedented’ event has already happened on each of the previous flips when the coin came up heads again. So, at each new spin the probabilities reset. The coin has no memory and each event has no effect on the next.

The same formula, P(A) =  N/0, applies when tossing more than one coin and calculating chances of particular events. Now the number of possible outcomes is that for each object, raised to the power of the number of objects. Thus with one coin there were two outcomes (H/T) but with two coins there will be four (22) permutations, which can be seen as TT, HT, TH, HH. With three coins, there will be eight possible outcomes (2x2x2).

Note that in calculating probabilities it is necessary to keep each outcome separate, even when they seem to be the same. Coin A showing Heads while Coin B shows tails is NOT the same outcome as the two coins coming down the other way round.

If we want to know the probability that one of three coins tossed will come down tails, we can see that there are three ways in which that event can occur, that it will be Coin A, Coin B, or Coin C that shows tails, or to put in binary form, THH, HTH, or HHT. Therefore the probability is three-eighths, or 37.5 per cent.

Tails-Tails-Tails

But the chance of all three coins showing tails is much less. There is only one TTT event, so the probability is one in eight or 13 per cent.

Wow.   Ok, a lot of thought went into that little treatise.   So at the end of the day, what does it all come down to?

Perhaps this clip, with Jim Carrey in “The Mask” mimicking Clint Eastwood’s famous Dirty Harry line: