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If you flip three fair coins, what is the probability that you'll get heads on the first two flips and tails on the last flip?

If you flip three fair coins, what is the probability that you'll get heads on the first two flips and tails on the last flip?

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Full solution

Q. If you flip three fair coins, what is the probability that you'll get heads on the first two flips and tails on the last flip?
  1. Coin Outcomes: Each coin has 22 possible outcomes, heads (H) or tails (T). So for three coins, the total number of outcomes is 2×2×22 \times 2 \times 2.
  2. Total Outcomes Calculation: Calculating the total outcomes: 2×2×2=82 \times 2 \times 2 = 8.
  3. Specific Outcome: We want the specific outcome HHTHHT. There's only one way to get this exact sequence.
  4. Probability Calculation: The probability of getting HHT is the number of ways to get HHTHHT divided by the total number of outcomes.
  5. Final Probability: Calculating the probability: 18.\frac{1}{8}.

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