10) What is the probability that the first number drawn on the Florence wheel is less than the first number drawn on the Naples wheel? (Remember that in the lottery, numbers from 1 to 90 are drawn).
(A) $\frac{44}{90}$
(B) $\frac{88}{179}$
(C) $\frac{44}{89}$
(D) $\frac{89}{180}$
(E) $\frac{1}{2}$.
10) The answer is $(D)$.

The probability that the two numbers are equal is $\frac{1}{90}$, and therefore the probability that they are different is $\frac{89}{90}$. In this case, the probability that the first is smaller than the second is equal to the probability that it is larger, and thus the sought probability is

$$
\frac{1}{2} \cdot \frac{89}{90}=\frac{89}{180}
$$