Explaining a coin toss to a friend problem

[CJ.Be]

I'm currently having trouble trying to explain a coin toss and it's probability to a friend.

The question is

A coin toss has a 50% chance to land heads. You flip the count twice. At least one of the tosses lands a head. What is the probability of both tosses being heads?

Now the correct answer is 1 in 3. For the following reasons.

Ok first coin is flipped, it has 2 options, heads or tails.

We know that we will get at least 1 heads in these 2 coin tosses.

First coin flipped gives us tails, so we know that the next coin has to be heads.

First coin is flipped but it gives us heads. Now we don't know if this was the one that was suppose to be heads or not. We flip the 2nd coin, it can either give us heads or tails. The 2nd coin gives us tails.

First coin is flipped giving us heads, second coin is flipped, it gives us heads.

Note how there are 3 outcomes, if we only know that one of the flips will give us a heads. So we have a 1 in 3 odds that when both coins are flipped, we get heads for both.

This is word for word of how I explain it to him. Now he is thinking that the answer is a 1 in 2 chance. Because we know one coin is going to be 100% heads. So you can just leave that one toss out, and just have the 2nd toss, which would be a 1 in 2 odds.

So I ask that someone might be able to help me to explain this to my friend in some easy more understandable way. Since he seems set in his answer.

 

[dalcde]

This is my way of solving the problem.

When you roll two dice, there are four possible scenarios:
1)HH
2)HT
3)TH
4)TT

Since at least one is a head, scenario 4 is rejected. Hence only 3 scenarios are possible. Only one is both heads (HH), so the probability is 1 in 3.

 

[M-quest]

To me your explanation is simple enough so I think you should tell your friend that a head is also possible on the 1st toss,we are 100% sure of getting atleast 1 head,not where that head will be i.e. 1st or 2nd toss.

 

[jeebs]

I like dalcde's answer, as it is very concise.

ask your friend to list the possible outcomes on a piece of paper, then tell him to get rid of the one that can't happen => 3 choices remain.

 

[blue_raver22]

Hey there, explaining probability can be tricky, but I'll try my best to help you out. So imagine you have a coin and you flip it twice. The first time you flip it, you have a 50% chance of getting heads and a 50% chance of getting tails. So far, so good. Now, let's say you flip the coin again, but this time, you already know that at least one of the flips will be heads. This means that you have either gotten heads on the first flip, or you will get heads on the second flip.

So, let's think about all the possible outcomes now. If you got heads on the first flip, then you have a 50% chance of getting heads on the second flip as well. If you got tails on the first flip, then you know that the second flip has to be heads since you were guaranteed at least one head. And if you got heads on the second flip, then you also have a 50% chance of getting heads on the first flip.

Looking at all these possible outcomes, we can see that there are three different ways in which we can get two heads in a row. And since there are only two possible outcomes for each flip, that means there are a total of four possible outcomes for two flips. This means that the probability of getting two heads in a row is actually 3 out of 4, or 3/4, which simplifies to 1/3.

I hope this helps your friend understand better. The key is to think about all the possible outcomes and how they are affected by the fact that you are guaranteed at least one head. Let me know if you have any other questions!