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

`P=(1)/(3), q=1-P=(2)/(3)`
Let x be a random variable for hitting the target.
`P(x ge 1) gt (5)/(6) " " N=`number of independent shots
`1-P(x=0) gt (5)/(6)`
`P(x=0) lt (1)/(6)`
`""^(N)C_(0)((1)/(3))^(0)((2)/(3))^(N) lt (1)/(6)`
`((2)/(3))^(N) lt (1)/(6)`
Minimum value of N = 5