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Unformatted text preview: Math 127A (Practice ﬁnal exam) December 6, 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?
(b) Find the probability that all four rolls are a ﬁve.
(c) Find the chance that at least one roll is a ﬁve.
(d) Find the probability that at least three ﬁves are rolled.
2. Three cards are dealt of the top of a deck. Find the chance that
(a) the second card is a queen;
(b) all three cards are queens;
(c) none of the cards is a queen;
(d) not all three cards are queen.
3. Four draws will be made from the box
once. 1 2 2 3 3 . Find the chance that a 2 is drawn at least 4. Suppose that there is a 50% chance that a child is male. Of all families that have 4 children, what
proportion have more boys than girls.
5. A multiple choice quiz has 25 questions. Each question has 5 answers, of which only one is correct.
A correct answer is awarded 4 points, 1 point is deducted for an incorrect answer. Suppose that a
student guesses the answers.
(a) Describe the box that models the student’s score on the quiz.
(b) What score should the student expect to get?
(c) If the passing score is a 50, then what is the chance of the student passing the quiz?
1 6. One hundred draws will be made from the box 2 3 4 5 6. (a) If the sum of the draws from the box is 321, then what is the average?
(b) If the average of the draws is 3.78, then what is the sum?
(c) Estimate the chance that the average of the draws is between 3 and 4.
7. A coin is tossed 25 times. Estimate the chance of getting 12 heads and 13 tails. 1 ...
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