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ProbSetOne - Rensselaer Electrical Computer and Systems...

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Rensselaer Electrical, Computer, and Systems Engineering Department ECSE 4500 Probability for Engineering Applications PS#1 Solutions February 12, 2010 1. (1.4) The experiment involves fl ipping a fair coin 3 times. The outcome of each coin toss is either a head or a tail. Therefore, the sample space of the combined experiment that contains all the possible outcomes of the 3 tosses, is given by = { HHH, HHT, HTH, HTT, THH, THT, TTH, TTT } . Since all the coins are fair, all the outcomes of the experiment are equally likely. The proba- bility of each singleton event, i.e. an event with a single outcome, is then 1 8 . We are interested in fi nding the probability of the event A , which is the event of obtaining 2 heads and 1 tail. There are 3 favorable outcomes for this event given by A = { HHT, HTH, THH } . Therefore, P [ A ] = P [ { HHT } { HTH } { THH } ] = P [ HHT ] + P [ HTH ] + P [ THH ] = 3 8 . Note that we are able to write the probability of the event A as the sum of probability of the singleton events (from Axiom 3) because the singlteon events of any experiment are mutually exclusive.

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ProbSetOne - Rensselaer Electrical Computer and Systems...

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