Question

The probability that a shooter hits a target is `(1)/(3)` The minimum number of triangles such that probability hitting the target atleast once is greater that `(5)/(6)` is equal to (a) 4 (b) 5 (c) 6 (d) 7 A. 6 B. 3 C. 5 D. 4 Select the correct answer from above options

Answer 1

Correct Answer - C 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.