If the probability of hitting a target by a shooter,

Question:

If the probability of hitting a target by a shooter, in any shot, is $1 / 3$, 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. 6

  2. 5

  3. 4

  4. 3


Correct Option: , 2

Solution:

$1-{ }^{n} C_{0}\left(\frac{1}{3}\right)^{0}\left(\frac{2}{3}\right)^{n}>\frac{5}{6}$

$\frac{1}{6}>\left(\frac{2}{3}\right)^{\mathrm{n}} \Rightarrow 0.1666>\left(\frac{2}{3}\right)^{\mathrm{n}}$

$\mathrm{n}_{\min }=5 \Rightarrow$ Option (2)

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