A coin is tossed three times. Calculate probability that the first and third - coin loses give heads as the outcomes, and what the outcome of the second toss

When a coin is tossed three times, each toss has 2 possible outcomes (Heads or Tails).
The total number of possible outcomes is $2 \times 2 \times 2 = 2^3 = 8$.
The sample space is:

We are looking for outcomes where the first toss is Heads (H) AND the third toss is Heads (H). The outcome of the second toss does not matter.
Let H represent Heads and T represent Tails.
The pattern for favorable outcomes is H _ H.
The possible outcomes that fit this condition are:

• HHH (First is H, Second is H, Third is H)
• HTH (First is H, Second is T, Third is H)

There are 2 favorable outcomes.

The probability is the ratio of the number of favorable outcomes to the total number of possible outcomes.

The probability that the first and third coin tosses give heads is $\boxed{\frac{1}{4}}$.