Question

Set $X$ is the set of all points $(x,y)$ in the coordinate plane such that $x$ and $y$ are both integers with absolute value less than $4$. If a point is chosen at random from set $X$, find the probability that this point will be located at a distance of $2$ units or less from the origin.

• A. $0.189$
• B. $0.227$
• C. $0.265$
• D. $0.314$
• E. $0.356$

Answer 1

The correct option is C $0.265$

$X$ could be $-3,-2,-1,0,1,2,3$, so there are $7$ choices for $x$. Likewise there are $7$ choices of $y$.

Altogether there are $7\times 7=49$ points that fit those requirement.

Of those only following point are distance of $2$ and less $(2,0),(1,-1),(1,0),(1,1)(0,2),(0,1),(0,0),(0,-1),(0,-2)(-1,-1),(-1,0),(-1,1)$ and $(-2,0)=13$ points.

So probability of points $=$ $\frac{13}{49}=0.265$