Question:
The least number of times a fair coin must be tossed so that the probability of getting at least one head is at least 0.8 is
The least number of times a fair coin must be tossed so that the probability of getting at least one head is at least 0.8 is
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The least number of times a fair coin must be tossed so that the probability of getting at least one head is at least 0.8 is
Updated On: Apr 15, 2026
- 7
- 6
- 5
- 3
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The Correct Option is D
Solution and Explanation
Step 1: Concept
Use the binomial distribution where $p = 1/2$ and $P(\text{at least one head}) = 1 - P(\text{no heads})$.
Step 2: Analysis
We need $1 - (1/2)^n \ge 0.8$, which simplifies to $(1/2)^n \le 0.2$.
Step 3: Evaluation
This is $2^n \ge 5$.
Step 4: Conclusion
The smallest integer $n$ satisfying this is $n=3$.
Final Answer: (d)
Use the binomial distribution where $p = 1/2$ and $P(\text{at least one head}) = 1 - P(\text{no heads})$.
Step 2: Analysis
We need $1 - (1/2)^n \ge 0.8$, which simplifies to $(1/2)^n \le 0.2$.
Step 3: Evaluation
This is $2^n \ge 5$.
Step 4: Conclusion
The smallest integer $n$ satisfying this is $n=3$.
Final Answer: (d)
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