Step 1 :The question is asking for the probability of tossing exactly one head when tossing three fair coins. The sample space provided shows all possible outcomes of this event.
Step 2 :To find the probability, we need to count the number of outcomes that have exactly one head and divide by the total number of outcomes.
Step 3 :The sample space for this event is \(['HHH', 'HHT', 'HTH', 'HTT', 'THH', 'THT', 'TTH', 'TTT']\).
Step 4 :The outcomes that have exactly one head are \(['HTT', 'THT', 'TTH']\).
Step 5 :So, the probability is \(\frac{3}{8}\).
Step 6 :Final Answer: The probability of tossing exactly one head when tossing three fair coins is \(\boxed{\frac{3}{8}}\).