What Are the Odds That a Given Cow Will Make It to the Super Bowl?

<p><pre><code> 66200000 / 17420000 * 20 = 76 </code></pre> This article is only true if every cow hide's resultant balls are sent to the exact same place. The superbowl could very well choose 76 different cowhide donors.<p><pre><code> 76 / 66200000 = 1 / 871 052.6 </code></pre> If that were the case, the odds would be (go figure) about 20x better of being chosen.<p>I bet the true probability is somewhere in between

Is it just me or did they miscalculate the odds here by trying to tell a story? It seems the only things that matter are:<p><pre><code> # of cows slaughtered annually: 66.2M / 1.99 = 33,266,331.7 # of footballs made per cow: 20 # of footballs used in the Super Bowl: 76 # of cows required to make the SB balls: 76 / 20 = 3.8 Odds a randomly slaughtered cow becomes a SB football = 33,266,331.7 / 3.8 = 1 in 8,754,297.82 </code></pre> What am I missing?

Related:<p>"... Thus there is a 1.8% chance that none of the molecules you are (still) holding in your lungs came from Caesar's last breath. And there is a 98.2% chance that at least one of the molecules in your lungs came from Caesar's last breath."<p>--John Allen Paulos, <i>Innumeracy</i> (1988) [1]<p>[1] <a href="http://econ161.berkeley.edu/movable_type/archives/001392.html" rel="nofollow">http://econ161.berkeley.edu/movable_type/archives/001392.htm...</a>