Answer: [tex]\dfrac{1}{216}[/tex]
Step-by-step explanation:
By binomial distribution formula:
[tex]P[X=r]=^nC_rp^rq^{n-r}[/tex] , where n is the number of trials , r is the number of success, p is the probability of success and q is the probability of failure.
Given: The probability of striking the bull's eye = [tex]p=\dfrac{1}{6}[/tex]
The probability of not striking the bull's eye = [tex]q=1-\dfrac{1}{6}=\dfrac{5}{6}[/tex]
Number of throw, n=3
Number of success, r=3
Now, the probability that you will strike the bull's-eye all 3 times is given by :-
[tex]P[X=r]=^3C_3(\dfrac{1}{6})^3(\dfrac{5}{6})^{3-3}\\\\=\dfrac{1}{216}[/tex]
