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A fair coin is tossed two times in succession. The sample space is​ shown, where H represents a head and T represents a tail. Find the probability of getting exactly one head.

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Part 1
The probability of getting exactly one head is
  
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​(Simplify your​ answer.)

1 answer

To find the probability of getting exactly one head when tossing a fair coin two times, we can first outline the sample space. The outcomes of tossing a coin twice can be represented as follows:

  1. HH (two heads)
  2. HT (first head, second tail)
  3. TH (first tail, second head)
  4. TT (two tails)

So, the complete sample space is:

  • HH
  • HT
  • TH
  • TT

Now, to find the outcomes that result in exactly one head, we can identify them from the sample space:

  • HT
  • TH

There are 2 outcomes (HT and TH) that correspond to getting exactly one head.

Given that there are a total of 4 outcomes in the sample space, we can calculate the probability as follows:

\[ \text{Probability of getting exactly one head} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{2}{4} = \frac{1}{2} \]

Therefore, the probability of getting exactly one head when tossing a fair coin two times is \(\frac{1}{2}\).