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Unformatted text preview: Probability and Statistics Course 92.386/407 Test 1 Time: 1 hour 30 minutes Please answer any five of the following six questions. Each question is worth 5 points Note: Numerical answers without supporting statements will not be given credit. 1.. a. Given P (A) = 0.59, P (B) = 0.30, and P (A n B) = 0.,21, find
i) P (Av B) ii) P (A n Be) iii) P (N V Be) iv) P(NnBe) h. Two fair dice are rolled, What is the probability that the number showing on one will be twice the numberappearingon the other? 2, A balanced die is tossed twice" IfA is the event that an even numbercomes up on the first toss, B is the event that an even number comes up on the second toss, and C is the event that both tosses result in the same number Are the events A, B, and C independent? Justify your answer. 3, Assume that 25% of all the cars in the state emit excessive amounts of pollutants, If the probability is 099 that a car emitting excessive amounts of pollutants will fail the state's vehicular emissions test, and the probability is 0.17 that a car not emitting excessive amounts of pollutants will also fail the test, what is the probability that a car which fails the test actually emits excessive amounts ofpollutants? 4,. Telephonenumbersin the U'.S. and Canada have 10 digitsdesignated as follows: 3.djgit area code number, whose first digit cannot be 0 or 1 Jdigit exchange number, whose first two digitscannot be 0 or 1 4digit linenumber, whose digits cannot be all 0 a, How many area codes are possible?
b. The area code for Boston is 617" Withinthis area code how many exchange numbers are possible? c. How many 7digit phone numbersare possible in the 617 area code? d. How manyphone numbers are possible in the U'S. and Canada? 5.. If six fair dice are rolled, what is the probability that a, all 6 faces are the same?
b. all 6 faces are different? 6. The probability density function for a continuous random variable is given by: f(x)
= k ..E, for 0 < x < 1 = 0 elsewhere. Find k and evaluate P (03 < X < 0.. 6). ...
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This homework help was uploaded on 10/27/2007 for the course MATH 4710 taught by Professor Jung during the Fall '05 term at Cornell University (Engineering School).
 Fall '05
 JUNG
 Statistics, Probability

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