A fair coin is tossed 6 times. What is the probability of getting a result in the 6^{th} toss which is different from those obtained in the first five tosses?
- A. \frac{7}{16}
- B. \frac{1}{16}
- C. \frac{1}{32} ✓
- D. \frac{1}{64}
Correct Answer: C. \frac{1}{32}
Explanation
For the 6^{th} toss to be different from the first five, the first five tosses must yield identical results. The only valid sequences are HHHHHT and TTTTTH. Since each sequence has a probability of (\frac{1}{2})^6 = \frac{1}{64}, the total probability is 2 \times \frac{1}{64} = \frac{1}{32}.
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