Conditional probability or independent events

[claudiocamera]

I have a doubt in the question below

In a box there are two coins one fair and one two headed. A coin is draw at random and tossed and the result is observed. The coin is returned to the box and the procedure repeated. Determine the probability that in the second toss the result is tail if it is known that head appeared on the first toss .

Since we are dealing with repeated trials, I see no influence from the first event to the second, and the answer requested is 0.75, am I right ?

If so, I cant understand the reason to this question refer to the first trial. Is there any chance of we have a conditional probability here?

 

[LouisSheffield]

The "first trial" might be to throw a student off.
You have not fallen for it, but you might want to check your math.
If the unfair coin is truly two-headed, the probability of tossing a tail should be 0.25.

 

[claudiocamera]

The "first trial" might be to throw a student off.
You have not fallen for it, but you might want to check your math.
If the unfair coin is truly two-headed, the probability of tossing a tail should be 0.25.

Ok, I exchange the probability to get a tail and a head in the second trial, so, is the answer really 0.25 for tail in the second trial , regardless the first one ?

What do you mean by

The "first trial" might be to throw a student off.

Maybe math is not the only problem that I had, I couldn't understand this sentence neither.

 

[LouisSheffield]

Sorry about that ...
Yes - 0.25, regardless of the first trial.

The part of the problem that stated "if it is known that head appeared on the first toss"
has no bearing on the solution. It is just excess information to test whether a student understands that it is irrelevant. The first coin was returned to the box. The past trial has no bearing on the future trial.

You spotted this, which is good.