Question:
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?
(A) 0.64 (B) 0.72 (C) 0.81 (D) 0.90 (E) 0.95
Answer:
(E)
Answer Key:
There are \(10^2=100\) possible ordered pairs.
That is, the cardinality of the set \(\{(S,T)\mid S,T\in\{1,...,10\}\}\) is 100.
There are five ordered pairs we don't want: \((1,1),(2,4),(4,2),(3,9),(9,3)\).
The probability that one integer will be the square of the other is \(\frac{5}{100}=0.05\).
The probability that neither integer will be the square of the other is \(1-0.05=0.95\).
I'd even recommend some of the classic papers or surveys of classic papers as reading material over a general subject test. For instance, why not a situation where students are given something like a research paper
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