Probability
Negative binomial; exactly 6 trials for 3rd success
MJMT_Full_Test_05
Grade 12
Question:
A shooter hits a target with probability $\frac{1}{4}$. She fires until she hits 3 times. Probability that she fires exactly 6 bullets lies in the interval
$(0.32,0.33)$
$(0.16,0.17)$
$(0.08,0.09)$
$(0.06,0.07)$
Step-by-Step Solution
Key Concept: 3rd success on 6th trial: first 5 have exactly 2 successes. $P=\binom{5}{2}(\frac{1}{4})^2(\frac{3}{4})^3\cdot\frac{1}{4}$.
$P\approx0.066\in(0.06,0.07)$.
Correct Answer: 4