Monday, December 20, 2010

What are the Chances?

The last three times I started my car, much to my amazement, Mariah Carey was singing her rendition of 'O Holy Night' that includes the one verse with her singing at least three octaves above my vocal range.  I have the car radio turned on one of the local stations playing Christmas carols, and this station is having their Top 100 Christmas Carol Countdown, which I've managed to hit at EXACTLY the same point, three times in three days.  Impressive right?
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Mariah's song was followed on all three occasions by "I Want a Hippopotamus for Christmas."  Not to sound too bah humbug about it, but I think the hippo song is one of my very least favorite Christmas songs.  Ben, however, loves this song so much that today when we got in the car he said (even before hearing the song again), "Mom, I want a hippopotamus for Christmas.   No, I'm just kidding.  I want Legos."

Now the really amazing thing to me is that all three errands occurred at different times each day.  What are the chances of catching the same carol in the countdown on the radio?  Really, I'm curious. Fortunately, I took a whole graduate level class in Probability and Statistics and we can easily figure it out (since this type of problem is from Chapter 1)!

(I'm just now realizing there is no equation editor in Blogger.  Bummer.) 

1) For the calculation, each instance of 'O Holy Night' is an independent event.
2) Since B101 is having their Top 100 countdown, the total number of possible songs to hear for each event is 100 songs.
3) The probability of hearing 'O Holy Night' one time when I turned on the radio is 1 in a 100 (P=0.01). The same for the second time and third time. 

Overall Probability= 1/P1 * 1/P2 * 1/P3
P = 0.000001

-OR-

The chances of hear this song right when I turn on the radio three times in three days is 1 in 1,000,000.
ONE IN A MILLION. 

I'm going to go buy a lottery ticket.  
(and change the radio station)

 

4 comments:

  1. actually, its not that lucky.
    i SWEAR that they have the same 20 songs on repeat. i ALWAYS hear the same 20 songs, despite the fact that there have to be HUNDREDS of Christmas songs!
    (If I hear "Sim-ply hav-ing a wonderful Christmastime" one more time...."

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  2. Normally I'd agree. I'm not even sure they have 20 songs. It's either the one you mentioned or something by Anne Murray....I'm assuming they actually made it through the entire 100 song countdown. But, maybe they were just playing #92 through #72 over and over and over again.... I wouldn't put it past them.

    Sweet new wheels, BTW!

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  3. Thanks for the yummy cookies... they were gone in about 3 minutes flat. I am checkin' out your blog (in case you didn't figure that one out) and I like it (I read your letter that accompanied the cookies)! 102.1 is probably the least creative radio, and it is not unusual for me to hear the same song traveling to and from home on my lunch break, so that's within the hour. So why do I keep it on that station? I just don't know! :-) l8r, g8r...your backyard buddy.

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  4. I think last year I had the same thing happening to me with the hippo song - I heard it every day! I actually know all the words to it, can you believe it? Then I mentioned it to someone, and they were like "what Christmas hippo song?" - they've never heard of it. This year - I have not heard it once! Plenty of Feliz Navidas though, I think I am going to puke next time I hear it.

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