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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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Outcomes of compound events

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?

Coin outcomes: Each coin has $2$ possible outcomes, heads (H) or tails (T).
First flip probability: The probability of getting heads on the first flip is $\frac{1}{2}$ .
Second flip probability: The probability of getting tails on the second flip is also $\frac{1}{2}$ .
Third flip probability: The probability of getting heads on the third flip is again $\frac{1}{2}$ .
Combined probability calculation: To find the combined probability of independent events, we multiply their probabilities: $(\frac{1}{2}) \times (\frac{1}{2}) \times (\frac{1}{2})$ .
Combined probability result: Calculating the combined probability: $\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8}$ .

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