We are being told by United Utilities that it is unsafe to walk, cycle or drive along the public road adjacent to Rough Crag because of the risk of rocks falling off the crag.  So can anyone here help me calculate (or validate my calculation) of the risk of someone being hit by a rock falling from this crag ?  In reality no rocks have fallen from the crag in the last 20 months, and the only known rock fall was during Storm Arwen, when a tree blew down that had been clinging to the crag, and when that tree fell it brought some pieces of rock down with its roots. But lets assume the following :

1 rock falls from Rough Crag each day.

That rock takes 1 second to hit the road.

I cycle past Rough Crag each day taking 1 second to pass the section where a rock might fall. 

What is the chances that I will be hit by a rock tomorrow ?

Well there are 86,400 seconds in a day.  So the chances that a rock falls from the crag is 1 : 86,400 in any particular second. And the chances that I happen to be cycling past in any given second is also 1 : 86,400.  Is it correct that to calculate the probability that the rock falls off the crag at exactly the same second that I happen to be cycling past I need to multiply these 2 probabilities together ?  So 86,400 x 86,400.  If so the chances that I will be hit by a rock falling off Rough Crag when I cycle past tomorrow is 1 : 7,464,960,000 (or 1 : 7.5 billion). Which, I hope you agree, is a risk worth taking.  

Now let’s assume that a rock only falls off Rough Crag during a very severe storm event, say once every 5 years.  What is the chances that I will be cycling past at that exact same moment (bearing in mind that I usually don't go out for a bike ride during very severe storms).  Is there a calculator big enough to calculate the probability of me being hit on the head by a rock falling from Rough Crag in those circumstances ? This maybe explains why, as far as I know, no cyclists have ever been known to have been hit on the head by rocks falling from a crag (any crag, anywhere in the world, at any time) as they were cycling past. 

Now let’s try to calculate the probability of me being hit by a car, bus or lorry whilst cycling along the diversion on the A591.  Well road traffic statistics for this stretch of road are pretty alarming, showing it is an accident black spot. And my personal experience bears that out as on the few occasions I have been brave enough to cycle along this stretch of the A591 I have felt very vulnerable to the vehicles that pass fast and close. Especially as I have no where to escape to as the whole road is hemmed in by dry stone walls and rock faces. And we know that almost 5,000 cyclists are seriously injured or killed each year on UK roads. Can we very confidently conclude that the risk of being severely injured or killed riding along the A591 diversion is massively greater than riding along the U7003 alongside Rough Crag ?  So if this is the case, why on earth is the U7003 closed (and proposals are now in place to make this closure permanent) ?

Please can someone / anyone check my workings here.  Or perhaps help come up with some more robust statistics on the relative risk of cycling along the quiet west side of Thirlmere compared to the busy twisting main road along the east side. 

Many thanks

Mark Hatton