2
$\begingroup$

Given that the radius of a dart board is uniformly distributed between 0 and 1, I throw a dart uniformly at random within a circle of radius 1. What is the probability of not hitting the dart board?

I have calculated the expected area of the dart board E(A) = π/3. Would it be correct to assume (1 - π/3)/π = 2/3 is the probability of not hitting the dart board? Or would I need to use integration given the continuous probability?


$\endgroup$

1 Answer 1

1
$\begingroup$

$\frac23$ is correct, and you can check it by integration

If the radius is $R$ than the conditional probability of not hitting is $\frac{\pi-\pi R^2}{\pi }=1-R^2$. So, since the density for $R$ is $1$ on the interval $[0,1]$, the overall probability is $$\int_0^1 (1-R^2)\,dR = \frac23$$

$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .