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# e3ps - Math 127A(Practice nal exam December 8 2010 The...

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Math 127A (Practice final exam) December 8, 2010 The practice exam has problems. It is about the same length as the actual exam. It does not represent every type of problem. 1. A die is rolled 4 times. (a) Are the rolls independent? Solution Yes (b) Find the probability that all four rolls are a five. Solution ( 1 6 ) 4 = 0 . 07% (c) Find the chance that at least one roll is a five. Solution The chance of at least one five is 100% minus the chance of none of them being fives, 1 - ( 5 6 ) 4 = 51 . 7%. (d) Find the probability that at least three fives are rolled. Solution Using the binomial formula we get that the chance of three fives is 4 3 × 1 6 3 × 5 6 1 = 1 . 54% The chance of four fives is 0 . 07% (calculated in the second part). Using the addition rule we get the probability of at least 3 fives is given by 1 . 54 + 0 . 07 = 1 . 61%. 2. Three cards are dealt of the top of a deck. Find the chance that (a) the second card is a queen; Solution chance the second card is a queen = chance first is a queen × chance second is a queen given first is a queen + chance first is not a queen × chance second queen given first not queen = 1 13 ×

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