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Engrd270 Section2 probabilities

# Engrd270 Section2 probabilities - (b Let A denote the event...

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Counting Number of ways of picking n objects from a collection if N objects is N C n = ! - ! ! N N n n Example: In poker, what is the probability of getting (a) A full-house (b) Three-of-a-kind (c) Two pairs a. Total number of full house handstotal number of all possible hands = 13x43x 12x42525 = , , , 3 7442 598 960 b. Total number of full house handstotal number of all possible hands = 13x43x 4x4x122525 = , , , 54 9122 598 960 c. Total number of full house handstotal number of all possible hands = 132x422x11x4525 = , , 1235522 598 960 =0.0475 d. The sample space S of an experiment is the set of all possible outcomes e. An event is a collection of outcomes i.e a subset of S f. Example: a college library has 5 copies of a text on reserve. Two copies(1,2) are first printing, the other 3 are second print. A student examines the book in random order, stopping only when a second printing has been selected. One possible outcome is (5) another one is (2,1,3) (a) List all possible outcomes (b)

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Unformatted text preview: (b) Let A denote the event that exactly one book is examined. What outcome are in A? (c) Let B= book 5 is selected. What outcome are in B (d) Let C= book 1 is not selected. What outcomes are in C a. S=(1,2,3) , (2, 1,3), (1,2,4) , (2, 1,4), (1,2,5) , (2, 1,5), (1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5), (3), (4), (5) b. 3,4,5 c. 125,215,15,25,5 d. 24,25,3,4,5 g. Example: h. A certain system can experience 3 different types of defects. Let Ai (i=1,2,3) denote the event that the system has defect of type i. Suppose that i. P(A1)= 0.12 j. P(A2)=0.07 k. P(A3)=0.05 l. P(A1UA2)=0.13 m. P(A1UA3)=0.14 n. P(A2UA3)=0.10 o. P(A1 and A2 and A3)= 0.01 (a) P(system does not have a type 1 defect (b) P(system has both a type 1 and type 2 defect (c) P(has type 1, type2 but not type 3 defect (d) P(at most 2 defects) a. 1-P(A1)=0.88 b. P(A1 and A2)= 0.06 c. P(A1 and A2 but not A3)= 0.06- 0.01=0.05 d. 1-0.01=0.99 p. q....
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