91Ó°ÊÓ

Sandy Koufax, one of the greatest baseball pitchers ever, struck out approximately one out of every four batters he faced. Assuming independence, what is the probability that the first batter Koufax strikes out is before the third batter he faces? (A) \((0.25)^{2}\) (B) \((0.75)^{2}\) (C) \(1-(0.25)^{2}\) (D) \(1-(0.75)^{2}\) (E) \(0.75+(0.75)(0.25)\)

Consider the following table of ages of U.S. senators: $$\begin{array}{|l|l|l|l|l|l|l|}\hline \text { Age (yr): } & <40 & 40-49 & 50-59 & 60-69 & 70-79 & >79 \\\\\hline \text { Number of senators: } & 5 & 30 & 36 & 22 & 5 & 2\\\\\hline\end{array}$$ What is the probability that a senator is under 70 years old given that he or she is at least 50 years old? (A) 0.580 (B) 0.624 (C) 0.643 (D) 0.892 (E) 0.969