Probability issues - a coin toss

This is not a comment on the first post, I am just commenting on the last ones saying for example that "5 heads in a row could easily indicate the coin is not random"

Do not forget that if that this post wouldn't have been made if the guy had gotten a more probable result.

Besides the odds for 5 heads is 3,125 %. But this would have been just as "special" if had gotten 5 tails. We are now up to 6,25 percent. Imagine that a lot of people might have some experience with tossing coins. They wouldn't have posted something like "At first I got two heads, then a tail, one head, and then a tail again." Maybe someone even would have said that the coin is not random if there were one head, then four tails and so on?

But if I were to guess I would also have betted on the recurring result happening again too. Because after all it is the same person tossing the coin all the times and he is more likely to throw it the exact same way that he did last time, than any other exact way.

The last part could perhaps have been explained better. Let me give an example. Imagine a bad dart player with a chance of 0,1 percent of hitting the bulls eye. Hitting the bulls eye is still the most likely event compared to hitting any similar sized area on the wall. Even tough he is bad he is at least trying to hit the bulls eye.

People tend to think that 50/50 means that out of all the tosses, half of them will be heads rather than should be heads.

I don't think that half of them should be heads either. I guess this is also a common misperception. If you for example toss the coin six times, it is considerably more likely that half of them will NOT be heads, than the opposite.

50/50 means that for any given toss, a head is as likely as a tail.

Consecutive tossing of a coin is a typical case of independent trials. For a single trial of tossing 50/50 is the right probability.

50/50 if there isn't a bias - i.e. a perfect coin and a perfect tosser.

Anyone got either of those at hand?

g_day,

I expect the former is a myth but the latter is quite common, especially here. :wink:

Time only goes in one direction--what has happened is a certainity, including tossing five heads in a row. If the coin is fair, what is going to happen next is a toss-up (literally)

Rap

Re: Probability issues - a coin toss


hello
every time you throw a coin the probibility of head appearing is 1/2 or 50%( if the coin is not biased). No one can be shore about it.

By now I think that maybe 10 people have said that the probability for a head is 50% for a single coin toss.

But you are forgiven "evolution", since you are "Just Hatched". And I feel its my duty as heavily outranking "Newbie" to welcome you to A2K.

All my coins are definitely imperfect.
As for the other thing, well there are plenty of those about.

It's true the coin has no memory but Murphy's Law has not been factored in.

The relevant corollary relates how much does one have to lose dependant on the outcome. Murphy's say damage will most likely be maximal.
(For some folks, any way they bet on the coin will be wrong

Re: Probability issues - a coin toss

I think most of us like to cling to preconceived notions as long as we have a choice. Accordingly, we tend to ignore that we are learning something new about a multiple coin tos as it proceeds.

Say you toss a coin twelve times. Before the first toss, the best bet is that you will get six heads and six tails. Then, for example, your toss begins with four tails in a row. Your rational response is to update your preconception, consider that the probability is still 1:1, and expect that the toss ends up eight tails, four heads. But updating preconception is difficult for and uncomfortable to the human mind, especially if they have already bet money on the old one. So many people won't update. Instead, they will continue to expect a 6:6 outcome and make up some excuse for not updating the preconception. For example, they might develop a vague feeling that `the coin owes me some heads', and this feeling comfortably closes the gap between expectation and reality.

Probability issues - a coin toss
When I was 17, someone street-proficient at dice taught me how to play "craps", where you commonly shoot for a 7 or 11. I noticed (and to his amazement) that I could make them roll the way I wanted, a surprising number of times. But I feel that this was because I could touch them. At the gambling casinos (which I've never visited), you aren't allowed to touch the dice.

I had a special method for doing it the way I did. Hmm... maybe if I transpose that method intrinsically, to other forms, such as the Texas Lotto? Maybe; we'll see. If I win, I might share a bit of it with the A2K members, here. Not that I play very much... I probably don't spend more than $5 per month on gambling games.

I always select 1, 2, 3, 4, 5, and 6. It's as likely a combination of numbers as any other.

True -- but other people are more likely to select "regular" combinations than random-looking ones. So this is a bad tactic when you play a lottery or something similar.

I used to do that too Drewdad, but Thomas is right. The fact that two of us here do that suggests we'll have to share our winnings but heaps of other "smart" folks like ourselves!