# Simple coin tossing question, confused on their answer

• mr_coffee
In summary, the conversation discusses a problem involving a coin being tossed 4 times with the outcomes of heads or tails being recorded. The question is how many times will exactly one head occur in the results. The solution involves 2^4 possible outcomes with 2 choices for each toss, resulting in 4 outcomes where exactly one head can occur. The reasoning for this solution is questioned, but it is determined that it was most likely an error in the book.
mr_coffee
Hello everyone. I"m just wondering why they solved the answer in this manner.

The question is:
A coin is tossed 4 times. Each time the result H for heads or T for tails is recorded. An outcome of HHTT means that heads were obtained on the first 2 tosses and tails on the second 2. Assume heads and tails are equally like on each toss.

Well they solved it this way:
There are 4 outcomes in which exactly one head can occur (since a string of one "T" and three "H"'s can have
the "T" in anyone of the string's four positions). So the probability of exactly one head is 4/2^4 = 1/4.

Okay I understand that there are 2^4 possible outcomes on 4 tosses, 2 chocies can happen, either a H or a T, so 2^4.

But Why did they say, since a string of one "T" and 3 "H"'s. If we are trying to find how many times you get exactly 1 head Why wouldn't they say the following:
since a string of one "H" and three "T"s can have the "H" in anyone of the strings for positions, such as HTTT, THTT, TTHT, TTTH, this shows its 4 ways, in which you will get exactly 1 head. I'm just confused on why they worded it that way or am I missing somthing?

Thanks

It's probably just an error in the book.

I thought so, but just wanted to make sure, the professor actually did the solution but either way it would come out to the same answer just making sure. thanks!

## 1. What is coin tossing?

Coin tossing is a simple game of chance where a coin is flipped and the outcome is either heads or tails.

## 2. What is the probability of getting heads or tails in coin tossing?

The probability of getting heads or tails in coin tossing is 50%, assuming the coin is fair and has an equal chance of landing on either side.

## 3. How many times should I toss a coin to get an accurate result?

It is recommended to toss a coin at least 30 times to get a more accurate result, as this will minimize the effect of any outliers or inconsistencies.

## 4. What is the difference between theoretical probability and experimental probability in coin tossing?

Theoretical probability is the expected probability based on mathematical calculations, while experimental probability is the actual probability observed through repeated trials.

## 5. Can the outcome of coin tossing be predicted?

No, the outcome of coin tossing cannot be predicted as it is a random event with equal chances of either outcome. Each toss is independent of previous tosses, so the previous outcomes do not affect the future ones.

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