The probability of a girl hitting a target is 1/2. How many times must she fire so that the probability of hitting the target at least once is more than 90%?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4
Suppose she fires n times. The target is hit at least once unless every shot misses:
\( \displaystyle P(\text{at least one hit})=1-\left(\frac{1}{2}\right)^n\gt 0.9 \)
\( \displaystyle \left(\frac{1}{2}\right)^n\lt 0.1 \)
Since \( \frac{1}{8}=0.125 \) and \( \frac{1}{16}=0.0625 \), the least n is 4.
CBSE Applied Mathematics (Class XII):
Binomial Distribution
