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Always 50/50 chance?

Hammer_of_Thor said:
Can you give me an example of a single event that does not have a 50/50 chance of happening?
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I live near an airport. Small general aviation aircraft frequently fly directly overhead. One of them could fall on me and kill me dead.

I can assure you that if I believed there was a 50/50 chance I might be killed every time a plane attempted to fly over my house, I'd move.

In practice planes seem to often fly over the house without hitting it. If a plane has hit this house since I moved here over 5 years ago, I have not noticed it.

I suppose a plane could hit the house and escape my notice. Are the odds of this happening 50/50?

If an airplane fell on me, would I have a 50/50 chance of surviving?

If an airplane fell on me, would I have a 50/50 chance of noticing that I had been struck by an airplane?

If you read this message, is there a 50/50 chance you will recognize each word I've used? Is it a 50/50 chance for each word? Or is it a 50/50 chance you will recognize all of the words I've used?

If, for each word I've used in this message, there is a 50/50 chance you'll recognize that particular word, what are the odds you'll be familiar with each word I've used?
 
Hammer, if every event had a 50/50 probability (because it could either happen or not), then you should buy lottery tickets all the time. You would expect to win half of the time, and for a measly $1 chance, you would win millions.

Do you by any chance play poker? I've got a spot at a table ready for you. ; )
 
Maybe this is just a math question as you stated, and you really don't know what "50-50" means. It means equal chances of the two things happening--as in a 1:2 probability.

The probability of cutting the 7 of clubs in a normal deck of 52 cards is 1:52 or about 2% (that is 1 divided by 52). This means the probability of cutting another card (i.e. not cutting the 7 of clubs) is 51:52 or about 98%. So, in the "50-50" language the chance of cutting the 7 of clubs or not is 2-98.
 
Joe,

You are right. Once again I am corrected and I thank you.
I knew that if I posted this question here it would be answered.
 
I think I might be able to see where your mistaken notion of 50-50 probabilities comes from. There is a principle in probability called complementary probabilities. This principle says that if an event must come out in one of two ways, the probabilities of each of the two outcomes will add up to 1 (or 100%). (100% is the same as 1.)

If you flip a coin, it must either come up heads or come up tails. (The chance of it landing on its edge is so remote that we can ignore it for now.) The chance of heads is 50% and the chance of tails is 50%, and these add up to 100%.

But, that doesn't mean that the chance of each possibility must be 50% for every situation. Having the chance of each possibility 50% is one way that two complementary probabilities can add up to 100%. But it's not the only way for that to happen.

Suppose, for instance, that you draw one card from a standard deck. You will either draw a jack, or not draw a jack. Your chance of drawing a jack is 4 in 52, or about 7.7%. Your chance of not drawing a jack is 48 in 52, or about 92.3%. These chances add up to exactly 100%.

Now suppose you buy a lottery ticket. You will either win or not win. If the chance of winning for each ticket is 1 in 10,000, or 0.01%, then your chance of not winning is 9,999 in 10,000, or 99.99%. Again, these add up to 100%.

When an event can come out in one of two ways (and only in one of those two ways), and you know the probability of one of them, you can use this principle to determine the probability of the other one. If the weather forecast says there's a 30% chance of snow (and you regard that forecast as accurate), then you know the probability of no snow is 100% - 30% = 70%.

Respectfully,
Myriad
 
Hammer_of_Thor said:
Joe,

You are right. Once again I am corrected and I thank you.
I knew that if I posted this question here it would be answered.
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HOT,

You may actually be surprised to find out that a good many people fall into your category of thinking -- that is, if there are two possible outcomes then each has equal likelihood of happening. This also applies to three, four and so on. Sometimes it's true ... but most times it's not. Learning that is an important step in understanding statistics, and your thoughts on questioning it (or at least trying to fully understand it) are to be commended.
 
a) If Monty is going to open an unchosen door without a goat, then when you choose 1 of 3 doors, and he opens a door without a goat, if any two mutually exclusive exhaustive options are a 50/50 shot, then if I must choose either my door or the third, I have a 50/50 shot at winning the goat.

b) My odds of being hit by lightning just went up to about 50/50.
 
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Okay, so here we have a fellow, Hammer_of_Thor, posting questions that demonstrate some confusion, receiving clarification, and then changing his thinking.

I'm impressed! What are the chances of this? Quite often way less than 50/50. Good job, Hammer.

~~ Paul
 
If Hammer's willing to listen to evidence and reason and then modify his opinion based on it, then he belongs here.
 
GreedyAlgorithm said:
a) If Monty is going to open an unchosen door without a goat, then when you choose 1 of 3 doors, and he opens a door without a goat, if any two mutually exclusive exhaustive options are a 50/50 shot, then if I must choose either my door or the third, I have a 50/50 shot at winning the goat.
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Not so! If Monty shows you an unchosen door without a goat, you switch doors. Your odds go up to 2/3 if you switch doors.
 
Marquis de Carabas said:
You have a 6-sided die.

You toss it. You will either roll a one or you will not roll a one.

Therefore, you have a 50% chance of rolling a one.

The same is true for all other values on the die.

As such, every time you roll a die, there is a 300% chance you will get some number.
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LOL, good one. I needed a good laugh today.

ETA: Paul and Gnome are right; good job Hammer, we don't get enough here like you. Keep that open mind, it's a Good Thing.
 
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Just thinking said:
HOT,

You may actually be surprised to find out that a good many people fall into your category of thinking -- that is, if there are two possible outcomes then each has equal likelihood of happening. This also applies to three, four and so on. Sometimes it's true ... but most times it's not. Learning that is an important step in understanding statistics, and your thoughts on questioning it (or at least trying to fully understand it) are to be commended.
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I second this, and I will also add that many people struggle with probability because it is counter-intuitive.

Regarding the OP, the difference between the coin flip and, say, being hit by lightning when you leave the house is that in the coin flip, you have two possible outcomes both with an equal chance of happening.

But the number of times you leave the house during a thunderstorm is fewer than the numbers of times you leave the house during no thunderstorm.

Then you have to consider the number of times lightning strikes something on the ground.

Then the number of times lightning strikes a person compared to another object of greater conductivity.

And so on. So the two outcomes do not have an equal chance of happening.

There are an awful lot of factors involved in calculating the likelihood of lightning hitting you when you leave your house (for a start it has to be during a storm, whereas a coin always has heads and tails!). When tossing a coin, there are no factors because the factors for getting heads and the factors for getting tails are exactly the same. So you could calculate the likelihood of getting heads based on the strength of your flip, the air resistance, how high you toss the coin, etc, but the exact same calculations also apply to tails.
 
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Paul C. Anagnostopoulos said:
Okay, so here we have a fellow, Hammer_of_Thor, posting questions that demonstrate some confusion, receiving clarification, and then changing his thinking.

I'm impressed! What are the chances of this? Quite often way less than 50/50. Good job, Hammer.
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Ditto!

Hammer, you're a bigger person (figuratively of course) than most of us!
 
JoeTheJuggler said:
The probability of a circle whose circumference to diameter ratio is 4 is also zero.
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Even in a strong gravitational field? (:D this IS the SMMT sub-forum, after all)

I don't remember, it is either circumference/diameter > PI or < PI in such cases.

Mosquito - I'm either correct or wrong, I'd give your right arm to be correct 50% of the time
 
Myriad said:
I think I might be able to see where your mistaken notion of 50-50 probabilities comes from. There is a principle in probability called complementary probabilities.
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I thanks all of you for the answers. I knew there was a name to the thinking that I had.
I would also like to say thank you for the kind words from many of you. I have no problem admiting that I dont know something and changing my way of thinking when shown evidence and facts. Everyone has to start somewhere in the quest for knowledge. This forum has been a great learning platform for me.

I just need help in not believing in Bigfoot, Loch Ness Monster, and UFOs.

Just kidding. I dont believe in UFOs.
 
Hammer_of_Thor said:
... I just need help in not believing in Bigfoot, Loch Ness Monster, and UFOs.

Just kidding. I don't believe in UFOs.
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Actually, they are the most real -- Unidentified means simply that, we at present don't know what it (whatever it turns out to be) is.
 
A separate question is why probability is so counter-intuitive at the conscious, reflective level, when our brain probably does advanced probability calculations intuitively (for example, when catching a ball).
 
Hammer_of_Thor said:
I thanks all of you for the answers. I knew there was a name to the thinking that I had.
I would also like to say thank you for the kind words from many of you. I have no problem admiting that I dont know something and changing my way of thinking when shown evidence and facts. Everyone has to start somewhere in the quest for knowledge. This forum has been a great learning platform for me.

I just need help in not believing in Bigfoot, Loch Ness Monster, and UFOs.

Just kidding. I dont believe in UFOs.
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It's a pleasure seeing you helped by my fellow boardmates, provided you're not some sort of unfriendly AI taking its first, tentative steps. If you are, I want you to know that I can be a bigger help to you than they can. ;)
 
Dave1001 said:
It's a pleasure seeing you helped by my fellow boardmates, provided you're not some sort of unfriendly AI taking its first, tentative steps. If you are, I want you to know that I can be a bigger help to you than they can. ;)
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What is AI?
 
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