2201 Prelim 1 Review

# 2201 Prelim 1 Review - Probability A number between 0 and 1...

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Unformatted text preview: Probability: A number between 0 and 1 that denotes the likelihood an event occurs &#2; If P(E) = 1, then E contains all possible outcomes &#2; Also known as sample space &#2; If P(E) = 0, then E contains no possible outcomes &#2; Also known as null set P(E) = (n e /n) as n approaches infinite &#2; Number of times that the event E occurs over the total number of repetitions of the experiment If I flipped a coin 300 times, and received 150 heads, then P(heads) = 150/300 = .5 P(E) = N e /N s &#2; The probability is equal to the number of outcomes in event E, divided by the total possible outcomes &#2; Only when each outcome is equally likely to occur I flipped a coin 3 times, what’s the probability that exactly 2 of them are heads? First list what the event is: &#2; E = {2 of 3 are heads} = &#2; {HTH, HHT, THH} &#2; Then list all the possible outcomes &#2; S = {TTT, TTH, THH, THT, HHH, HHT, HTT, HTH} So the probability that exactly 2 are heads is P(E) = E/S, = 3/8 Independent : Two events are considered independent if the occurrence of one does not influence the occurrence of the other. &#2; Tossing a coin and talking, no effect on each other &#2; Mutually Exclusive : Two events are considered mutually exclusive if they cannot both happen at the same time, one or the other &#2; Standing and Sitting down Intersection &#2; E F ∩ : E intersect F, is the event that contains the outcomes of both E and F E F E F ∩ Intersection of the sets {1,2,3} and {2,3,4} &#2; {2,3} &#2; If and only if E & F are independent then the Probability of the intersection is the product of the probabilities &#2; P(E) = .5 If E and F are independent, P(E F) ∩ = &#2; P(F) = .4 P(E)*P(F) = (.5)*(.4) = .2 Union &#2;...
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2201 Prelim 1 Review - Probability A number between 0 and 1...

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