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In a certain game of tennis, Alex has a 60% probability to win any given point against Blake. The player who gets to 4 points first wins the game, and points cannot end in a tie. What is Alex's probability to win the game?

You have a radio that measures incoming signals from deep space. You expect to hear pulses with amplitude 0 (no activity) and amplitude 1 (from two separate neutron stars which pulse independently with the same probability over any small discrete time interval). However, about 16% of the time, you hear a pulse with an amplitude of 2.

Is this alien communication or simultaneous pulses? And how can probability help answer this question?

An economist analyzing factors that led to the Great Recession finds that many companies that speculated on mortgage-backed securities believed that the mortgage-backed securities were safe investments, and the probability of a default (failure or refusal to pay the mortgage) on any one of them was reasonably small, so the probability of a massive default was extremely small. What are some flaws of this reasoning?

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