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 `(5)/(6)` is

Options

A. 6
B. 3
C. 5
D. 4

Answer

C

Explanation

The probability of hitting a target at least once =1-(probability of hot hitting the target in any trial)
`=1-overset(n)""C_(0)p^(0)q^(n)`
where n is the number of independent trials and p and q are the probability of success and failure respectively.
[by using binomial distribution]
Here, `p=(1)/(2)` and `q=1-p=1-(1)/(3)=(2)/(3)`
According to the question, `1-overset(n)""C_(0)((1)/(3))^(0)((2)/(3))^(n)gt(5)/(6)`
`rArr ((2)/(3))^(n) lt 1-(5)/(6)rArr((2)/(3))^(n)lt (1)/(6)`
Clearly, minimum value of n is 5.