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

• A. 7
• B. 6
• C. 5
• D. 3

Hint:

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

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
Use the binomial distribution where $p = 1/2$ and $P(\text{at least one head}) = 1 - P(\text{no heads})$.
Step 2: Evaluation
We need $1 - (1/2)^n \ge 0.8$, which simplifies to $(1/2)^n \le 0.2$.
Step 3: Final Calculation
This is $2^n \ge 5$.
Step 4: Conclusion
The smallest integer $n$ satisfying this is $n=3$.
Hence, the Answer is: (d)