STUDY GUIDE- Exam 2

# STUDY GUIDE- Exam 2 - Probability Independent events:...

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Probability Independent events: (whatever outcome we are interested in) events are independent if the occurrence of one does not affect the occurrence of another. Ex. Successive flip of fair coin Sample with replacement (put it back into pool, to potentially be sample again)= independent Dependent events: events are dependent if occurrence of one affects the occurrence of another. Ex. Drawing cards from a deck WITHOUT putting them back in after each draw Sampling without replacement= dependent Mutually exclusive: events that cannot occur at the same time Ex. Rolling (1, 2, or 3), rolling (4, 5 or 6) cannot have both outcome at the same time. Collectively exhaustive: at leas one of the events must occur Ex. Rolling (1, 2, 3, 4, 5, or 6) on a die Advanced Addition Rule *NON-Mutually Exclusive: P (A or B) = p (A) + p (B) – p (A and B) Ex. What is the probability of drawing either an Ace or a Heart from a fair deck of cards? (13 each suit, 4 of each rank) A= Ace B= Heart, p(A and B)= 1/ 52 bc Ace of Hearts is one card. p(A or B)= p(A) + p(B) – p(A and B) p(A or B)= (4/52) + (13/52) – (1/52) p(A or B) = 16/52 Conditional Probability: describing the chance of something happening, given a certain situation (it depends on that particular condition) multiple events p(B A) probability of B given A (A will happen) ex. Flipping 3 heads in a row, given you flipped the coin three times **NOTE: p(B A) ≠ p(A B) Advanced Multiplication Rule: (dependent events): p(A and B)= p(A) * p(B A) (independent events): p(A and B)= p(A) * p(B) (bc p(B A) is = to p(B) bc p(A) is independent. There is no given A) Computing Conditional Probabilities: p(B A)= p(A and B)/ p(A) Ex. What is the probability of being dealt a pair of Kings (“pocket Kings”) for your first two down cards in Texas Holdem? “AND” problem (p(dealt one King AND another King) Two events are dependent (bc only a limited number of Kings in deck, one you get one of them) p(A and B)= p(A) * p(B A) p(A)= 1 st King= 4/52

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p(B)= 2 nd King= 3/51 p(B A)= 3/51 p(A and B)= (4/52) * (3/51)= 12/2652= 1/221 Discrete probability: distribution of a variable that can only take on certain values. - can’t get 1.5 heads off 2 flips, or 2.5 heads. - X-axis: possible values - Y-Axis: probability of each value o Ex. “# or heads on two flips” Continuous probability: distribution of a variable that takes on a range of values. (our observation can take on any value in that range) -X-axis: possible values - Y-axis: density (basically, probability) of each value Ex. “age at which child first crawls…” - NOTE: with these, can only speak of probability of an interval In general, sampling distributions are always going to be continuous Expected value: average total “expected” over many random events. (depends on what is being measure [i.e. dice roll]) take the sum, across each possible outcome, of (probability of outcome * outcome value) Ex. Dice rolling
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## This note was uploaded on 04/08/2008 for the course PSYCH 110 taught by Professor Burt during the Spring '08 term at Vermont.

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STUDY GUIDE- Exam 2 - Probability Independent events:...

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