If prayers go unanswered....?

Yes, the idea that this is an unlikely event is being miscalculated very badly.To determine how many time this would have to occur before it becomes statistically significant the following has to be done.How many people are humming a tune before they turn on a car radio?
What are the total number of tunes that they might be humming and the radio may play? (this is not simply the total number of all tunes -- remember there is such a thing as "top 40").
How many of these people should get a hit at any time?
Given these numbers of people how frequently might we expect 2, 5, 10 in row from all of the people.This is a slightly more out of the ordinary example of the picking up the phone to find that the person you were going to phone is on the line which hasn't rung yet.Given the number of times that you phone a small subset of all possible people this is almost guarenteed to happen every so often. It is not a surprise or a mystery or psychic or any such thing.

No, there is not one person humming a tune. There are 1,000's or 10,000's in north america. If you don't consider that this is exactly like being astonished that someone won the lottery with odds of many millions to one against that number being picked. WIth many people humming and turning on radios someone has some perhaps not to small chance of getting several hits in a row.The lack of understanding of this is what supports a nice little fraud in the area of stock promotion.You recieve a promotion for a newsletter that lists 5 stocks to buy. The newsletter is very expensive (say 1,000 $ for 4 quarterly issues). You ignore it.Some weeks later you recieve another promotion showing how those 5 stocks have gone up substantially since the last promotion. It also give you 5 more stocks to buy.Guess what? A few weeks later another promotion points out that the second set of stock also went up and you would have more than paid for the subscription if you had only bought them. More spectacular results are suggested (with all the usual disclaimers in the fine print).This is a scam that is actually perpetrated. How is it done?Another way to look at this is:How many times in your life, have you been humming when you turned the radio on? How many of these were "misses" and how many were "hits"? What are the odds of any one hit?This message has been edited by NosyNed, 04-09-2005 01:00 PM

The probability that this will happen somewhere is one figure which requires a consideration of all the possible events.The probability that this will happen to one person who is preselected is another figure.However, that one individual that matched the broadcast songs was not preselected. They were selected after the event occured.Which is really surprising? Mr. Smith won the lottery or Mr. Smith won the lottery after having been written up in newspaper headlines as next weeks lottery winner.The first case probability calculations requires knowledge of all the different possible events. The second requires only that we know the odds against Mr. Smith's single lottery number being picked.The probability that someone will win the lottery is, on many draw days, pretty near 1. The chances that Mr. Smith's number will come up after he has been selected as the winner is several millions to one. If it happened even once one might begin to suspect fraud in the process.

While hoping that a statistician will show up here I'll go over this in more detail. This will seem a bit odd but be patient it is relevant. The event happened by then it has a probability of 1.I think it is possible to determine the probabilites involved and therefore an estimate of how statistically unlikely this event is. Getting the 'right' answer would be very difficult since we will have to estimate a lot of things that we are not going to want to spend the effort of actually measuring.Let's have a go at that and while doing so see if there is any connection to the lottery circumstance.Let's make up some numbers to start with:If the station plays 100 different songs and an individual hums one of those at random the odds that a single trail will produce a hit is, obviously, 1 in 100.I suggest that the individual is very likely to be humming one of the pop songs (the 100) as that is why that person picks that station and the ones played are the most likely to be hummed.(hidden in here is a chance that the 100 songs are biased with the "top 40" played more often than other and the individual being more likely to be humming one of those but I am ignoring that for the moment).If we take raw probabilities the odds of hitting the same song in only 5 trails (one after the other with no intervening misses) are (1/100 )^5This is obviously a terribly small probability(about 1 in 10^-10). It is exactly like the probability of picking 5 numbers on a lottery when there are 50 numbers to choose from ( 1/50 ) ^5 as an example.So the chances of one particular individual getting 5 song hits are not very large.The issue is that you are asking what the probability that this will happen somewhere. You did not specify the individual in advance so the events have to consider ALL the individuals.Let's make up some more numbers:There are 10 million individuals turning on their radios while humming and they do this 5 times per day.That suggests, in my simple minded view, that a 5 song hit will not happend for about 10,000 days or 30 years.I think it is safe to say (based on these estimates) that as many as 5 in a row is pretty dammed unlikely. But we have to be sure that we are given the precise set of circumstances.A huge issue is:
Are we asking what the odds are of it happening to one preselected individual or are we asking what the odds are of it happening so some individual out of many?