What don't I get about coin tossing?

[Intervenient]

I've never had a basic probability course before, so I've only been able to get my hands on a few materials relating to the subject.So let's say there are 5 coin tosses. The probability of getting heads 5 times in a row is .5^5, or 1/32.

But since coin tosses are independent of each other, each time the coin is tossed, there's an equal chance of it being heads, as it is tails. So shouldn't the probability always be .5? Doesn't 5 heads in a row, have the same probability of heads, tails, heads ,tails, heads?

What piece of the puzzle aren't I getting :/
Edit: There are 32 different possible outcomes, hence 1/32. I get that because it's independent it's either heads or tails, and not due up. So I guess the question is how they relate.

 

[pwsnafu]

The prob of "head, head, head, head, head" is exactly the same as "head, tail, head, tail, head" which in turn is the same as "head, head, tail, head, head" which is the same as "tail, tail, tail, tail, tail" and so on.

There are 32 possible results to five coin tosses, and each is just as likely as the rest. They must add up to 1. So the prob must be 1/32.

 

[SW VandeCarr]

The important point is that probability is a measure of uncertainty. Any particular sequence of 5 tosses, predicted in advance, has a 1/32 probability of occurring assuming a fair coin. After the sequence is generated, it no longer makes sense to talk about the probability of that sequence. The probability of an event that has already occurred is 1. The probability of generating the same sequence again is 1/32.

 

[chiro]

Like pwsnafu said, there are 32 states instead of 2, so the probability is distributed over 32 (i.e. 1/32) instead of 2 (1/2).

 

[blue_raver22]

I can understand your confusion about coin tossing and probability. The key concept to understand in this scenario is the concept of independent events. Each coin toss is an independent event, meaning that the outcome of one toss does not affect the outcome of the next toss. This is why the probability of getting heads or tails on each toss is always 0.5 or 50%.

However, when we look at a series of coin tosses, the overall probability of a specific outcome changes. In your example of 5 coin tosses, the probability of getting heads 5 times in a row is indeed 1/32. This is because the probability of getting heads on the first toss is 0.5, and the probability of getting heads on the second toss is also 0.5. But when we combine these probabilities, we use the multiplication rule, which states that the probability of two independent events occurring together is the product of their individual probabilities. In this case, it is 0.5 x 0.5 x 0.5 x 0.5 x 0.5, which equals 0.03125 or 1/32.

In short, the key concept to understand is that the overall probability of a specific outcome in a series of independent events is calculated by multiplying the individual probabilities. I hope this helps clarify your understanding of coin tossing and probability.