Is probability logical?

[Yogi DMT]

I understand how simple probability situations function but logically, it doesn't make sense.

Scenario: A coin is tossed and there is a 50% of it landing on heads and a 50% chance that it will land on tails. The probability of getting heads/tails twice in a row is 25% (.5 x .5). This 25% probability refers to the situation as a whole (not to any particular toss in the sequence).

So, a coin is tossed and lands on heads. The next toss is either 50% heads or 50% tails. To overall probability of the situation says that tails is then more likely an outcome, because that would satisfy the higher probability (h+t = 50%, h+h = 25%, t+t = 25%) which would of course be more likely. So after the first toss results in heads, the second tossed is supposedly more likely to be tails when you look at the overall situation regardless of the probability of the 2nd toss alone is half and half... According to probability, the first toss and the probability of the 2 tosses combines determines a different probability for the second toss other than the 1/2 and 1/2 probability of heads and tails.

I know i'm missing something, why is this?

[Fido]

There is a 99.999 percent chance that the coin will land... Probability is logical because when you know the probabilities you know what will happen, and what will happen, effect following cause, you know what is going to happen...

[prothero]

Originally Posted by Yogi DMT

I know i'm missing something, why is this?

Once you know the outcome of the first toss. The probablity of the second toss is .5 heads and .5 tails as it is for any indiviudal toss.

It is only in sequences of events (3,4,5 or more tosses) where the outcome of no event has yet been determined that the stochastic probabilities patterns can be applied.

Your quandry is a common misunderstanding.

If the first toss is already known to be heads, then the probability of two heads is now 50% not 25% like it was before the first toss occurred.

[kennethamy]

Originally Posted by Yogi DMT

I understand how simple probability situations function but logically, it doesn't make sense.

Scenario: A coin is tossed and there is a 50% of it landing on heads and a 50% chance that it will land on tails. The probability of getting heads/tails twice in a row is 25% (.5 x .5). This 25% probability refers to the situation as a whole (not to any particular toss in the sequence).

So, a coin is tossed and lands on heads. The next toss is either 50% heads or 50% tails. To overall probability of the situation says that tails is then more likely an outcome, because that would satisfy the higher probability (h+t = 50%, h+h = 25%, t+t = 25%) which would of course be more likely. So after the first toss results in heads, the second tossed is supposedly more likely to be tails when you look at the overall situation regardless of the probability of the 2nd toss alone is half and half... According to probability, the first toss and the probability of the 2 tosses combines determines a different probability for the second toss other than the 1/2 and 1/2 probability of heads and tails.

I know i'm missing something, why is this?

Yes, you are missing something. You are committing the notorious Gambler's fallacy.

Gambler's fallacy - Wikipedia, the free encyclopedia

[Emil]

Originally Posted by Yogi DMT

I understand how simple probability situations function but logically, it doesn't make sense.

Scenario: A coin is tossed and there is a 50% of it landing on heads and a 50% chance that it will land on tails. The probability of getting heads/tails twice in a row is 25% (.5 x .5). This 25% probability refers to the situation as a whole (not to any particular toss in the sequence).

So, a coin is tossed and lands on heads. The next toss is either 50% heads or 50% tails. To overall probability of the situation says that tails is then more likely an outcome, because that would satisfy the higher probability (h+t = 50%, h+h = 25%, t+t = 25%) which would of course be more likely. So after the first toss results in heads, the second tossed is supposedly more likely to be tails when you look at the overall situation regardless of the probability of the 2nd toss alone is half and half... According to probability, the first toss and the probability of the 2 tosses combines determines a different probability for the second toss other than the 1/2 and 1/2 probability of heads and tails.

I know i'm missing something, why is this?

The probability of the second coin does not change. Indeed you're flirting with the Gambler's Fallacy.

[kennethamy]

Originally Posted by Emil

The probability of the second coin does not change. Indeed you're flirting with the Gambler's Fallacy.

It's not flirting. It is a marriage.

[Yogi DMT]

Originally Posted by kennethamy

Yes, you are missing something. You are committing the notorious Gambler's fallacy.

Gambler's fallacy - Wikipedia, the free encyclopedia

Basically haha, makes more sense now. Thanks

[Kroni]

Everyone is right, the odds change once the sequence of occurrences before it have been given.

Probability is a strange concept, though. On the surface it is very logical, but many times in the real world things don't play out the way the odds say they should. If you have pocket aces and someone else has pocket 2s, the 2s can still win if they hit 3 of a kind. What is the driving force that determines whether or not an event will follow the odds?

[kennethamy]

Originally Posted by Kroni

Everyone is right, the odds change once the sequence of occurrences before it have been given.

Probability is a strange concept, though. On the surface it is very logical, but many times in the real world things don't play out the way the odds say they should. If you have pocket aces and someone else has pocket 2s, the 2s can still win if they hit 3 of a kind. What is the driving force that determines whether or not an event will follow the odds?

A single event? Chance.

[Kroni]

In order for probability to be perfectly logical, the results of chance should equal the probability odds when you look at the entire series of events. If the odds of pulling one card from the deck that is a diamond are 25%, then logically when you add up every time anyone has pulled one card from a deck in all of history, exactly 25% of them should wind up being diamonds.
There's no way we can accurately say whether or not this is true, but it seems that many times things do not turn out this way.