Question

You are throwing darts at a dart board. You have a 1/ 6 chance of striking the bull's-eye each time you throw. If you throw 3 times, what is the probability that you will strike the bull's-eye all 3 times?

Answer 1

Cube 1/6

Answer: 1/216
Or 0.46% chance.

Answer 2

Answer:
`(1)/(216)`

Explanation:

By binomial distribution formula:

`P[X=r]=^nC_rp^rq^(n-r)` , 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 =
`p=(1)/(6)`

The probability of not striking the bull's eye =
`q=1-(1)/(6)=(5)/(6)`

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 :-

`P[X=r]=^3C_3((1)/(6))^3((5)/(6))^(3-3)\\\\=(1)/(216)`