More clarifications.

Author: bwbeach

Diff for: calculation.ipynb

@@ -29,6 +29,11 @@
     "is the same thing as a monthly failure rate of 1.0 (100%), and is the same thing as a daily\n",
     "failure rate of 0.0333 (3.33%).\n",
     "\n",
+    "If you're running a shop that requires 10 widgets, and the failure rate is 12,\n",
+    "you'll go through a lot of widgets, and you'll have to keep getting replacements.\n",
+    "Over the span of a year, you can expect to buy 120 new widgets as replacements so you\n",
+    "can always have 10 running.\n",
+    "\n",
     "## Probability of Failure\n",
     "\n",
     "Assuming that the probability of separate failures is independent, the probability of failure \n",
@@ -57,6 +62,10 @@
     "\n",
     "If you add up the infinite sequence of probabilites, it will add up to 1.0.\n",
     "\n",
+    "In practice, looking at one of the widgets in your shop, this means that there's a 13.5% chance\n",
+    "you won't have to replace it in the year.  There's a 27% chance you'll replace it once, a\n",
+    "27% chance you'll replace it twice, an 18% chance you'll replace it three times, and so on.\n",
+    "\n",
     "To calculate the probability of zero failures, you can simplify the formula:\n",
     "\n",
     "$$\\text{probability of 0 failures} = e^{-\\lambda} \\: \\frac{\\lambda^0}{0!} \\: = \\: \\: e^{-\\lambda}$$\n",
@@ -144,6 +153,10 @@
     "* $P$ is the probability of a shard failing at least once in $R$ days\n",
     "* $D$ is the durability of data over $R$ days: not too many shards are lost\n",
     "\n",
+    "With erasure coding, your data remains inact as long as you don't lose \n",
+    "more shards than there are parity shards.  If you do lose more, there\n",
+    "is no way to recover the data.\n",
+    "\n",
     "One of the assumptions we make is that it takes $R$ days to repair a failed\n",
     "shard.  Let's start with a simpler problem and look at the data durability\n",
     "over a period of $R$ days.  For a data loss to happen in this time period,\n",