Solutions - 5070-02

(1) Identify the binomial structure:

Each day has probability $\frac{1}{50}$ of showing Wisconsin’s flag, independently of the other days, and probability $\frac{49}{50}$ of showing a different state’s flag. There are $\left(\genfrac{}{}{0px}{}{3}{2}\right)=3$ ways to choose which 2 of the 3 days have the Wisconsin flag.

---

(2) Evaluate:

$$\begin{array}{c}P[\text{2 of 3 days}]=\left(\genfrac{}{}{0px}{}{3}{2}\right)\cdot {\left(\frac{1}{50}\right)}^2\cdot \frac{49}{50}\\ \\ \gg \gg 3\cdot \frac{49}{\mathrm{125,000}}\gg \gg 0.001176\end{array}$$