combinatrix & probabilities

Question

probabilities have always been something tough to comprehend for me, may be someone can help me on this. So here's the problem:

Bob tosses a coin but can't see the result, his friend John can see it, but chooses to tell the result totally at random.

What the probability that john gives a correct result ? (there are 4 distinct events) 25% ?

Is this problem different from the probability of having two consecutive tail or heads ? Seems it is since in that case, the probability is conditional to having obtained a tail or head before...

But it seems also identical, in the sense that a correct result is the realisation of two identical coin toss...

Sorry if it's confusing, I'm no math guru.

cheers -A

Answer 1

The $4$ distinct events are:

• John sees "head" and says "head"
• John sees "head" and says "tail"
• John sees "tail" and says "head"
• John sees "tail" and says "tail"

John gives a correct result in $2$ out of $4$ events, so the probability for that is $\frac24$.

This is indeed equivalent to the probability of having $2$ heads or $2$ tails out of $2$ attempts.