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M118 Sample Final 2

# M118 Sample Final 2 - 1 Not including the empty set how...

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1. Not including the empty set, how many subsets does the set { 3 , 4 , 5 } have? (A) 5 (B) 6 (C) 7 (D) 8 (E) 2 5 - 1 (F) none of the others 2. Lurlee has 3 hats and 4 umbrellas, and it is a very cold, rainy day. He decides to take with him two hats and one umbrella. In how many ways can he choose these items? 3. A gaggle of 130 geese wants to decide which way to travel this Fall. There are 80 geese which would agree to go South, 63 which would agree to go North, and 5 which would not agree to go anywhere. How many geese would agree to go South, but would not agree to go North?

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4. A fair coin was tossed 12 times, and the outcomes were: 3 heads and 9 tails. When the same coin is tossed a 13th time, what is the probability the oucome will be tails? 5. Professor Umbuggio likes to have his TI2003 calculator with him every day. However, on some days he remembers to take it with him, and on others he forgets. If he remembers it one day, he is equally likely to remember or to forget it the following day. If he forgets it one day, he is sure to remember it next day. This situation is an example of a Markov chain; state 1= remembers, state 2= forgets. Find the transition matrix for this chain. (A) bracketleftbigg 1 0 . 5 . 5 bracketrightbigg (B) bracketleftbigg . 5 . 5 0 1 bracketrightbigg (C) bracketleftbigg . 5 . 5 . 5 . 5 bracketrightbigg (D) bracketleftbigg . 5 . 5 1 0 bracketrightbigg (E) bracketleftbigg . 5 1 . 5 0 bracketrightbigg (F) none of the others 6. After spending many hours rolling a six-sided die, Averell Dalton decides that it is not a fair die. In fact, a three is twice as likely as any other outcome. What is the probability of rolling a three with this die? (A) 1/6 (B) 1/7 (C) 1/8 (D) 2/9 (E) 2 / 7 (F) none of the others
7. A student uses a tutoring center where he meets one of two tutors, Humpty and Dumpty. Humpty is at the center 60% of the time, and Dumpty 40%. Moreover, Humpty can solve a problem with probability .8, while Dumpty can solve a problem with probability .7. Our student cannot solve a problem, and he is planning to visit the tutoring service. What is the probability that he will find the solution during this visit?

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M118 Sample Final 2 - 1 Not including the empty set how...

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