This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Determine the total number of possible outcomes. When a coin is tossed three times, each toss has 2 possible outcomes (Heads or Tails). The total number of possible outcomes is 2 × 2 × 2 = 2^3 = 8. The sample space is: S = \ HHH, HHT, HTH, THH, HTT, THT, TTH, TTT \ Step 2: Identify the favorable outcomes. 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) Step 3: Count the number of favorable outcomes. There are 2 favorable outcomes. Step 4: Calculate the probability. The probability is the ratio of the number of favorable outcomes to the total number of possible outcomes. P(first H and third H) = Number of favorable outcomesTotal number of possible outcomes P(first H and third H) = (2)/(8) Step 5: Simplify the probability. (2)/(8) = (1)/(4) The probability that the first and third coin tosses give heads is (1)/(4). Drop the next question!