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

If you flip three fair coins, what is the probability that you'll get a tail on the first flip, a head on the second flip, and another tail 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 tail on the first flip, a head on the second flip, and another tail 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 a tail on the first flip is 12\frac{1}{2}.
  3. Second flip probability: The probability of getting a head on the second flip is also 12\frac{1}{2}.
  4. Third flip probability: The probability of getting a tail 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: 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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