Two players, A and B , alternately and independently flip a coin and the first player to obtain a head wins. Assume player A flips first. (a) If the coin is fair, what is the probability that A wins? (b) Suppose that \( \mathrm{P}(\mathrm{head})=\mathrm{p} \), not necessarily \( 1 / 2 \). What is the probability that A wins? (c) Show that for all \( \mathrm{p}, 0<\mathrm{p}<1, \mathrm{P}(\mathrm{A} \) wins) \( >1 / 2 \) (Hint: Try to write \( \mathrm{P}(\mathrm{A} \) wins) in terms of the events \( \mathrm{E} 1, \mathrm{E} 2 \ldots, \ldots \) where \( \mathrm{Ei}= \) \{head first appears on ith toss \( \}) \)

B \( \begin{array}{c}0,5 l \\ 0,35 \mathrm{dl} \\ 0,035 \mathrm{dl} \\ 3,5 \mathrm{dl} \\ 35 \mathrm{cl}\end{array} \)

Which statement best explains the major difference between economic imperialism and colonialism? A. Unlike colonialism, economic imperialism can be practiced by both communist and capitalist countries. B. Unlike colonialism, economic imperialism does not require a country to take direct control over a territory. c. Unlike colonialism, economic imperialism allows a country to dominate a territory thousands of miles away. D. Unlike colonialism, economic imperialism brings some economic benefits from one country to another territory!

Consider the following sum. \[ 16_{\text {seven }}+13_{\text {seven }} \] Determine the sum using base 7 \( 16_{\text {seven }}+13_{\text {seven }}=\square \) seven

25. What does Malcolm say about their foes?

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