A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is $\frac{1}{100}$. What is the probability that he will win a prize (a) at least once (b) exactly once (c) at least twice?

Question

$\begin{array}{1 1} (a)\; 1 - \large(\frac{99}{100})^{50} \quad (b)\; \large\frac{1}{2} (\frac{99}{100})^{49} \quad (c)\;1 - \large(\frac{99}{100})^{49}(\frac{149}{100}) \\(a)\; 1 - \large(\frac{99}{100})^{50} \quad (b)\; \large\frac{1}{2} (\frac{49}{100})^{49} \quad (c)\;1 - \large(\frac{49}{100})^{49}(\frac{99}{100}) \\(a)\; 1 - \large(\frac{99}{50})^{25} \quad (b)\; \large\frac{1}{2} (\frac{49}{50})^{49} \quad (c)\;1 - \large(\frac{49}{50})^{49}(\frac{49}{100}) \\ (a)\; 1 - \large(\frac{99}{50})^{25} \quad (b)\; \large\frac{1}{2} (\frac{99}{100})^{49} \quad (c)\;1 - \large(\frac{49}{50})^{49}(\frac{149}{100}) \end{array}$