**Solution:**

When two coins are tossed simultaneously, the possible outcomes are:

* Head-Head (HH)
* Head-Tail (HT)
* Tail-Head (TH)
* Tail-Tail (TT)

Out of these four outcomes, only one outcome has been eliminated by the given condition that the first coin has shown a head. Therefore, the sample space is reduced to:

* Head-Tail (HT)
* Tail-Head (TH)
* Tail-Tail (TT)

The probability of the second coin showing a tail given that the first coin has shown a head can be found using conditional probability formula:

P(Tail on second coin | Head on first coin) = P(Tail on second coin and Head on first coin) / P(Head on first coin)

* P(Tail on second coin and Head on first coin): The only outcome that satisfies this condition is Tail-Head (TH). Therefore, the probability of this is 1/4.
* P(Head on first coin): The outcomes that satisfy this condition are Head-Tail (HT) and Head-Head (HH). Therefore, the probability of this is 2/4 or 1/2.

Now, using the conditional probability formula:

P(Tail on second coin | Head on first coin) = P(Tail on second coin and Head on first coin) / P(Head on first coin) = (1/4) / (1/2) = 1/2

Therefore, the probability of the second coin showing a tail given that the first coin has shown a head is 1/2 or 0.5.

**Conclusion:**

The probability of the second coin showing a tail given that the first coin has shown a head is 1/2 or 0.5.

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