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# 28h - Discrete Mathematics Finite Probability 28-2...

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Introduction Finite Probability Discrete Mathematics Andrei Bulatov Discrete Mathematics – Finite Probability 28-2 Experiments and Outcomes Experiment: Tossing a coin Outcomes: {heads, tails} Experiment: Rolling a dice Outcomes: {1,2,3,4,5,6} Experiment: Rolling two dice Outcomes: {1,…,6} × {1,…,6} or {A {1,…,6} : |A| 2} Experiment: Buying 3 lottery tickets (out of 100,000) Outcomes: 3-element subsets of {1,…,100000} Discrete Mathematics – Finite Probability 28-3 Sample Space and Events The set of all outcomes of an experiment is called the sample space Sometimes we are interested not in a single outcome, but an event that happens in several outcomes Examples: Get heads at least 3 times when tossing 5 coins Win a prize in lottery Get 2 aces in a poker hand Discrete Mathematics – Finite Probability 28-4 Events Let S be the sample space of a certain experiment. An event is any subset of S Examples: Experiment: Tossing 2 coins Sample space: S = {heads,tails} × {heads,tails} Event: Get exactly 1 heads A = {(heads,tails),(tails,heads)} Experiment: Rolling 2 dice Sample space: S = {1,…,6} × {1,…,6} Event: The sum of the dice is 6 A = {(1,5),(2,4),(3,3),(4,2),(5,1)} Discrete Mathematics – Finite Probability 28-5 Probability In all our experiments each of the possible outcomes has the same

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28h - Discrete Mathematics Finite Probability 28-2...

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