Conditional probability gives the chance of tossing a coin and getting three heads as 0.5*0.5*0.5 = 0.125

As I wrestle with this I ask myself what the chances of having three sons in a row are? 0.5*0.5*0.5 = 0.125

Now bear with me, if you have already got 2 sons what is the probability of having a third son in a row? 0.5? or 0.125?

As I wrestle with this and the maths that goes with it I ponder the Puritan ban on games of chance. As I understand it, their objection was that there was no such thing as chance!

As I wrestle with probability - the fact that the chances can indeed be calculated does indeed suggest that there is no "chance". Or am I under a misapprehension.

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Eoghan
member,Thurso Baptist Church
Scotland

specialist subject: Creationist Genetics (Bottleneck effect of the Ark)
interests: holiness (practical theology)
member of Biblical Creation Society (available as a guest speaker in the far north of Scotland)

The probability of having a third son is 0.5. It's not related to the first two conceptions.

"Chance" only exists because we don't have knowledge of all factors. If we knew the workings of everything in the universe, as God does, we wouldn't take chance into account.

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Jonathan
Audio Engineer
Reformed Anabaptist
Ohio

Moroni's magical glasses of proper interpretation:

If you have no children - the chances of you having three sons in a row are
0.5*0.5*0.5 = 0.125

If you already have one son the chances of having another two sons are
0.5*0.5 = 0.25

If you have got two sons (which has a 0.5*0.5=0.25 chance) then a third son will be a chance of 0.5

What starts as an outside chance "improves" to a 0.5 chance

Every time you flip the coin there is (theoretically) a 50-50 chance it will be heads/tails. Having three heads in a row is providence.

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Jim
1689 LBCF
Independent Bible Church
North Texas, USA

That's because you now have more knowledge than you did when you started. If you had known how many children (and what gender) before you started, then the probabilities would have been either 100 or 0; the "chance" factor simply represents what you don't know.

This is actually incorrect. The probabilities that have been calculated all assume independence, which is essentially a mathematical assumption that the outcome of one random experiment does not give you information or affect the outcome of the other experiments. However, that is not the case with children. My wife has received significant training in the areas of pregnancy and childbirth, and there are in fact biological factors at work that could make it more likely to have a son or daughter. In fact, the probability of having a son is actually a little more than .5 (if you simply look at the proportion of births that are boys compared to girls). As far as the conditional probability, the more sons (or daughters you have), in general, the less likely it is that you will have children of the opposite sex. In these cases, there is usually a biological factor at work.

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Joshua F
Layman
Mountain View Community Church (Missionary Church Denomination)
Johnstown, CO

This is related to the gambler's fallacy. The gambler, after a string of 'bad luck' feels that he is 'due' for some 'good luck'. In fact, the chance of him having a winning hand remains exactly the same as before.

I think you are a bit off here. When we calculate chance, we are calculating the average rate (as you approach infinity) of correct predictions of the outcome. This, of course, assumes a 'fair' dice or shuffle of the cards.

However, I would say that the flip of a fair coin is only random in a practical sense, because we are unable to precisely measure the rotation and force of the toss. If we were able to measure with such precision (as God is able), and understand the physics of the throw, a correct prediction would theoretically be possible 100% of the time.

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Tim Lindsay
member, Covenant Reformed Presbyterian Church, Halifax, NS, Canada
Living in Cape Town, South Africa
"under the Southern Cross, at the foot of Table Mountain, not far from the Cape of Good Hope"

If you roll a dice along an x-y axis and ensure that one of the spinning faces is a 6, AND you do it gently - then you should have a 1 in 4 chance of getting a six!

-----Added 11/5/2009 at 10:01:42 EST-----

nobody has commented on precisely why puritans banned games of chance

The odds each time you flip a coin to get a head or tail is 1 in 2, or .50 -- no previous event will have an effect on the next flip

The odds to get, say, three heads in a row on a coin toss is indeed .5*.5*.5 = .125

Flipping coins and having young'uns are two different things -- the predominance of male or female children pretty much comes down through the father's side.

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JWithnell
Member Bethel OPC
Virginia
http://learningyesican.blogspot.com/

Another example of the probability changing with more data.

-----Added 11/5/2009 at 10:57:03 EST-----

Because there were people like you who "gamed the system" to ensure that everyone else's money found its way into your pocket.

No, conditional probability is the probability of event B happening given that event A has occurred. B|A For your question of children, given that you have already had two sons, the probability would seem to be .5 that you would have a third son ... the reason I say "seem" is that there may be some condition that would predispose y'all to having sons rather than daughters. Without getting into TMI, suffice it to say that while the general probability of having a male child is about .5 (if you are having a child) it is not proven that a particular couple will have a .5 probability (and the actual is not exactly .5, but slightly higher for conceiving a male).

General probability of 3 sons in a row is the probability of a single event, it has a probability of .5 to the 3rd power or 1/8.

In the sense that God has foreordained whatsoever comes to pass, the occurrence of any event is fixed from before the creation of the world. While that is true, that does not mean that we can know what way a coin toss will land on any occurrence that is not "fixed". While I fully understand that many lives have been ruined by gambling, I look at it like any other activity which is done for recreation. It can be abused. But because something can be abused, doesn't mean it must be abused. Playing a simple game of cards (which in most cases includes both skill and chance) is no more sinful than taking a bike ride.

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Brian Withnell
Deacon, OPC
Leesburg, Virginia

You cannot train for war in the midst of a battle. Prepare before the battle starts; if the battle is long and hard, you will wish you had.

Others can "do the math," as they say in the States.

The Puritan view is based on the fact that the whole disposing of the lot is from the Lord. We should not play with providence as it is a taking of the Lord's name in vain. The Puritans insisted that we should be wise observers of providence and not accredit anything to blind chance or fate. Are you willing to pray for a blessed outcome from that dice or coin? If not, you can't do it to the glory of God.

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Yours sincerely,


"Illum oportet crescere me autem minui."

If you like probability stuff, here's a fun exchange I had with some profs some time ago having to do with children...

Reformed Apologist: Sometimes We Do Agree...

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Ronald W. DiGiacomo / Ruling Elder
Christ Presbyterian Church (OPC)
Elkton, Maryland

http://reformedapologist.blogspot.com

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Andrew S.
Covenant Presbyterian Church (OPC)
Abilene,TX

There was a wonderful article in the Scientific American which explained conditional probability started with a scottish lawyer. What he was trying to show was the way evidence stacked up to show a case probable.

Interesting to note that criminal law looks for evidence that proves guilt. In employment law however the level is much lower and is "on the balance of probability".

I simplify grosly here but I leave a lawyer to make it more complicated and less understandable.

-----Added 11/6/2009 at 10:23:36 EST-----

I would love you to expand on this! I always though of gambling as immoral wheras the puritans seem to have viewed it as irreligous? (a casting aside of the doctrine of providence)

Given the context of "card counting" it does seem to be applied maths. I believe most casinos now operate 7 decks where they used to use 4 decks of cards, as an anti card-counting measure.

Which part--the aspect of money being put on the line, or the nature of card and/or dice games?

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Daniel
PCA
Memphis, TN

Gambling of itself would have been considered immoral on numerous fronts, e.g., earning money by means which God has not ordained; but playing games of chance on any level was certainly seen as irreligious because it plays with providence. If God is certainly bringing all things to pass, and saints earnestly believe God is working all things together for their good, and prayer seriously seeks God's blessing in the course of His providence, then one should not roll that dice for no other reason than personal fun.