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The probability that a shooter hits a ta...

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

6

B

3

C

5

D

4

Text Solution

Verified by Experts

The correct Answer is:
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.
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