JEE PYQ: Probability Question 44
Question 44 - 2019 (11 Jan Shift 1)
If the probability of hitting a target by a shooter, in any shot, is $\frac{1}{3}$, then the minimum number of independent shots at the target required by him so that the probability of hitting the target at least once is greater than $\frac{5}{6}$, is:
(1) 3
(2) 6
(3) 5
(4) 4
Show Answer
Answer: (3)
Solution
$1 - \left(\frac{2}{3}\right)^n > \frac{5}{6} \Rightarrow \left(\frac{2}{3}\right)^n < \frac{1}{6}$. For $n=5$: $\left(\frac{2}{3}\right)^5 = \frac{32}{243} < \frac{1}{6}$. So $n = 5$.
BETA
