From Question 5 the practice book of the GRE math subject test:
Sofia and Tess will each randomly choose one of the $10$ integers from $1$ to $10$. What is the probability that neither integer chosen will be the square of the other?
Choices: (A) $0.64$, (B) $0.72$, (C) $0.81$, (D) $0.90$, (E) $0.95$
The only pairings I see using only integers from $1$ to $10$ are:
- $1$ and $1$
- $2$ and $4$
- $3$ and $9$
This means the probability of the above events occuring are $\frac 3{10} \cdot \frac 3{10} = \frac 9{100}=0.09$. I took the complement of this and found that the probability of this event not happening is $0.91$. However, this is none of the above choices.
Best Answer
There are five choices which fit the description: $(1,1),(2,4),(4,2),(3,9),(9,3)$. Any option which is not one of these is fine. This leaves $95$ out of $100$ choices, so $0.95$ is right.