Coin toss question

Hello,

I have a question that I am getting confused by. The question is: Suppose a fair coin is thrown three times. What is the probability of the event that heads comes up on the first toss or the second toss?

So the sample space has 8 elements and 6/8 of these contain a Heads on the 1st and/or 2nd toss.
I thought at first the probability to get H on 1st or 2nd is 1/2 x 1/2 so it equals 1/4 but now I am not sureI

I did another attempt where I multiplied the probability of getting a Heads multiplied by 1/3, which is the number of trials
So then for that I got 1/2 x 1/3 + 1/2 x 1/3 = 1/3

I think the OR part of this question is making me overthink. Please let me know what is the proper way to approach this.
Thanks!

funnybabe said:

I have a question that I am getting confused by. The question is: Suppose a fair coin is thrown three times. What is the probability of the event that heads comes up on the first toss or the second toss?
So the sample space has 8 elements and 6/8 of these contain a Heads on the 1st and/or 2nd toss.
I thought at first the probability to get H on 1st or 2nd is 1/2 x 1/2 so it equals 1/4 but now I am not sureI

Click to expand...

Here is the outcome set:
\(\displaystyle \begin{array}{*{20}{c}} H&H&H \\
H&H&T \\
H&T&H \\
H&T&T \\
T&H&H \\
T&H&T \\
T&T&H \\
T&T&T
\end{array}\)
The first six rows are favorable outcomes, so the probability is 6/8.