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If you flip three fair coins, what is the probability that you'll get a head on the first flip, a tail on the second flip, and another head on the third flip?

If you flip three fair coins, what is the probability that you'll get a head on the first flip, a tail on the second flip, and another head on the third flip?

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Full solution

Q. If you flip three fair coins, what is the probability that you'll get a head on the first flip, a tail on the second flip, and another head on the third flip?
  1. Coin outcomes: Each coin has 22 possible outcomes, heads (H) or tails (T).
  2. First flip probability: The probability of getting heads on the first flip is 12\frac{1}{2}.
  3. Second flip probability: The probability of getting tails on the second flip is also 12\frac{1}{2}.
  4. Third flip probability: The probability of getting heads on the third flip is again 12\frac{1}{2}.
  5. Combined probability calculation: To find the combined probability of independent events, we multiply their probabilities: (12)×(12)×(12)(\frac{1}{2}) \times (\frac{1}{2}) \times (\frac{1}{2}).
  6. Combined probability result: Calculating the combined probability: 12×12×12=18\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8}.

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