What are the Odds?

As you probably know by now, two of the candidates for the post of Bishop Suffragan in Los Angeles are in sexual relationships outside of marriage, exactly the kind of thing that Rowan in his recent letter said was simply not acceptable for a priest, let alone a Bishop. Speculation is rife as to the likelihood of either candidate being elected (there are two available posts).

Speculate no more!! Thanks to the magic of mathematics, we can now calculate exactly what the chances are!! Let’s go.

  • The probability of both candidates being elected is (2/6 * 1/5) – 2 candidates out of 6 for the first post, and once the first candidate is elected the second candidate is 1 of 5.
    • This gives us a probability of 0.066r or 1 in 15
  • The probability of at least one candidate being elected is (2/6 * 4/5) + (4/6 * 2/5) – 1 candidate elected for first post with neither for second OR neither elected for first post with one for the second.
    • This gives us a probability of  0.533r or 16 in 30
  • Total probability that at least one of the two candidates will be elected is therefore 0.6 or 3 in 5

Let’s not stop there though. The Diocese of Minnesota has nominated a woman living in a sexual relationship outside of marriage for their vacant Episcopal post. So, even if Los Angeles pull back from the brink, Minnesota might do the deed.

  • The probability of electing a candidate who would put a cat amongst the pigeons in Minnesota or Los Angeles is 0.6 + (2/5 * 1/3) – Odds of electing a candidate in Los Angeles plus odds of electing one in Minnesota if Los Angeles doesn’t.
    • This gives us a probability of  0.733r or 11 in 15

What does that all add up to? Odds on, with the likelihood of a candidate being elected who is living in a sexual relationship outside of marriage being almost 3 in 4, we’re in for a fun autumn.

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9 Comments on “What are the Odds?

  1. Well the Episcopal Church still has gifts to give the world. SChadenfreude is apparently one of its gifts. It provides to the Anglican Communion and the Church at large the same joy that your mad uncle Francis provides at family gatherings. He’s a pain to deal with, but the stories he provides delight both friends and family for generations.

  2. So, Peter+, Did you learn all this math in school or at the races?

    Being an ardent Dick Francis fan (always looking for a rescuer) though not a horsewoman, I loved reading about steeplechasing and the pace of his books was an escape from the drudge of housewifery.

    I could hardly wait for Christmas every year when he would publish another book. His books were addictive, though perhaps not so much as the cliff-hanger Anglican follies and soap opera has become for me!

    Anyway, your math ability is impressive! Thanks for sharing.

  3. Peter,

    I must quibble with your last calculation. The likelihood of Chicago electing a problematical candidate do not depend on whether LA does so or not. So your estimate of (2/5 * 1/3) actually lowers the odds slightly.

    So, making that correction, we find the likelihood of Minnesota or LA to be .6 + 1/3 = 9/15 + 5/15 = 14/15 = 0.933, a bit closer to the sure thing, eh?

    Unless you were using the “or” in the sense that one and only one diocese does the deed. Then you would be correct. But if you are using “or” in the sense that one or both dioceses do the deed, then my figure is correct.

    Cheerful results brought to you by Maths!

    Allen

    • Au contraire. We are calculating the probability that at least one of the three candidates is elected. Therefore, the final calculation for MN is conditional on whether a candidate has already been elected in Los Angeles or not.

  4. Agreed but I might suggest the following:

    In probability, it is often easier to calculate the negative statement, i.e., if you want to know the probability that at least one bishop is homosexual, first calculate the probability that no homosexual bishop candidates are chosen and subtract that from 1.

    Suppose the candidates in L.A. are A, B, C, D, E, F with A and B are homosexual candidates. Then the probability that the heterosexual candidates are 4 out 6 for the first choice and then since one has selected from C through F, there are five choices left with 3 heterosexuals. Thus the probability that LA will have heterosexual bishops is (4/6) x (3/5) = 2/5 or 0.4. The probability that a heterosexual is chosen in Minnesota is obviously 2/3.

    Thus, the overall probability that all heterosexuals will be chosen is (2/5) x (2/3) = 4/15. The probability that a homosexual candidate will be chosen is 1 – (4/15) = 11/15.

  5. Peter,

    That was precisely my point. It hinges on your usage of the word “or” in this sentence:

    The probability of electing a candidate who would put a cat amongst the pigeons in Minnesota or Los Angeles….

    Had you said “…either Minnesota or Los Angeles…” that would have made it quite clear what you were doing. But the “or” with no qualifier means either one or both could do the deed.

    Isn’t English fun! Especially when compounding it with probability calculations!!

    But all in good fun.

    Robroy’s solution is much simpler and does fit what you said you intended in your reply to me.

    Cheers!

    Allen

  6. Two points –

    first of all these probabilities are meaningless: the trials are not independent. Given it is ECUSA and the events of GC2009, a bookmaker would not give any odds for no gays being elected.

    second – and most important – it simply does not matter at all whether or not more gay candidates will be elected (or whether the receive consents)

    The commnion, after all, demanded Robinson’s resignation; the resignation of all gay priests and laypeople in positions of responsibility; the cessation of all gay blessings – way back in ’98 – and the Windsor report wording meant that. The communion demanded a moratorium that included nomination, that was rescinded last week and broken this week. And on and on and on.

    Perhaps it should be a “Fun Autumn” because TEC is opening a second front in the UK, or because – on the basis of GC 2009 another 10% of parishes and 2 or 3 diocese have to leave TEC!

    But this – is nothing but a sideshow at a soap opera.

  7. I would agree that probabilities are irrelevant because we aren’t going to line up a hundred TEC’s and run an experiment.

    If Peter+ might permit me to stray tangentially somewhat with regards to the misconceptions of probabilities and how I use it in my Christian medical practice.

    When patients ask me, “Doc, what are the odds that I will be here a year from now?” I give them a standard line, “It will either be 0% or 100%. None of us knows the time or the hour. We might get hit by a Mack Truck tomorrow. But we should treat each day as a blessing.”

    The use of the phrase, “no one knows the time or the hour” and the term “blessings” are what the Christian Medical and Dental Associations’ Saline Solution program calls “faith flags.” These are non-threatening verbal cues that you are a person of faith. Some patients miss the faith-flags, some ignore them, and for some this opens up a very necessary line of communication.

    If anyone is interested in faith flags, etc, Walt Larimore M.D. has a book for physicians called “The Saline Solution” and for general people in the workplace, “Going Public with Your Faith: Becoming a Spiritual Influence at Work.” Walt is a big hero of mine.

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