Have you ever had a double-yolk egg?
This is what one looks like...the pair of smaller yolks flanked by two large ones. It's always a fun little surprise. Just another mundane morning, frying up some eggs for breakfast, and then...boink! Something you don't expect to see.
I say always a fun surprise, but it has only happened to me twice. Just the other morning and then once before about a year or so ago.
Back in grad school I worked about a half-year rotation on a project measuring vitamin D receptors in the chorioallantoic membrane of japanese quail embryos. I cracked open hundreds of eggs on that project, if not thousands, and never once saw a twin. Though I did see a couple of monsters; sad little misshaped embryos with strange developmental defects.
In any event, since this is "statistics semester" and I was thinking about upcoming probability lectures, I wondered how lucky I must be to have witnessed two twin yolks in my lifetime!
The internet, which never disappoints and which I have no reason to doubt, says the random chance of seeing one of these even once is 1 in 1000.
When I run this little script
[pDY <- dbinom(2, size=10,000, prob=0.001) #Yes, I seem to like to eat a lot of eggs]
through the R machine to see how lucky I must have been to witness this twice it says my luck is 1 in 22,400. Which seems pretty nice.It makes me feel lucky.
I have also done something else that is is considered a reasonably rare feat, I have scored a hole-in-one in golf not just once, but 3 times!
The internet says the "risk" of a random single hole-in-one for somebody like me is 1 in 12,500. I actually have better reason to believe this probability than I do for the double yolk frequency, because the value of the hole-in-one probability comes from a company that makes a living betting that people WON'T score one. So they probably have a good idea what the probability of a random hole-in-one truly is, since their livelihood depends on it.
I ran a similar script through the R machine to calculate the probability that I could have had 3 holes-in-one. I've been playing golf for 30 years, and guesstimate I've played 20 rounds per year over that period. Some years more than others.
[pHOI <- dbinom(3, size=600, prob=0.00000008)]
The R machine says the probability of me accomplishing this three hole-in-one feat is actually very, very, very low. About 1 in 54 trillion.
Now I'm feeling even luckier!
So what are the chances that somebody like me would have seen 2 double yolk eggs AND have 3 holes-in-one playing golf? That's a simple joint probability( pHOI * pDY ) and that value comes out to a whopping 1.2 octodecillion!!
Had I known I was actually this lucky I would have bought one lottery ticket last week. This all assures me that I had a very good chance at winning the $1.5 billion jackpot.