Question:
The probability of a bomb hitting a target is 1/2. The least number of bombs required to have a probability of hitting the target more than 0.9 is:
The probability of a bomb hitting a target is 1/2. The least number of bombs required to have a probability of hitting the target more than 0.9 is:
Show Hint
Hitting a target is a Bernoulli trial; "at least one" problems use the complement of "none".
Updated On: Apr 8, 2026
- 4
- 3
- 5
- 2
Show Solution
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The Correct Option is A
Solution and Explanation
Step 1: Concept
$P(\text{at least one hit}) = 1 - P(\text{no hits}) = 1 - (1/2)^{n}$.
Step 2: Analysis
$1 - (1/2)^{n}>0.9 \Rightarrow (1/2)^{n}<0.1 \Rightarrow 2^{n}>10$. For $n=3$, $2^{3}=8$. For $n=4$, $2^{4}=16$.
Step 3: Conclusion
The least number of bombs required is 4.
Final Answer: (A)
$P(\text{at least one hit}) = 1 - P(\text{no hits}) = 1 - (1/2)^{n}$.
Step 2: Analysis
$1 - (1/2)^{n}>0.9 \Rightarrow (1/2)^{n}<0.1 \Rightarrow 2^{n}>10$. For $n=3$, $2^{3}=8$. For $n=4$, $2^{4}=16$.
Step 3: Conclusion
The least number of bombs required is 4.
Final Answer: (A)
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