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Test 1 & Solutions

Test 1 & Solutions - Probability and Statistics Course...

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Probability and Statistics Course 92.386/407 Test 1 Time: 1 hour30 minutes Please answer anyfive of the following six questions. Each question is worth 5 points Note: Numerical answers without supporting statements will not be given credit. 1 .. a. GivenP (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(NnB e ) h. Two fair dice are rolled, What is the probability that the number showing on one willbe twice the numberappearingon the other? 2, A balanced die is tossed twice" If A is the event that an evennumbercomesup 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
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