Final_A_Fall_06_091206 - MATH 333A Probability Statistics...

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MATH 333A: Probability & Statistics. Final Examination (Fall 2006) Score December 20, 2006 NJIT Instructors : M. Bhattacharjee, R. Dios, A. Jain Must show all steps for each problem to receive full credit. I pledge my honor that I have abided by the Honor System. ___________________ (Signature) 1. At a certain gas station, 40% of the customers buy regular gas, 35% buy plus gas, and 25% buy premium gas. Of those customers buying regular gas, 30% fill their tanks. Of those buying plus gas, 40% fill their tanks. Of those buying premium gas, 70% fill their tanks. (5 points each) a. What is the probability that the next customer will buy plus gas and fill the tank ? b. What is the probability that the next customer fills the tank ? c. If the next customer fills the tank , what is the probability that regular gas is bought ? d. Let G denote the event that the next customer buys plus gas and F denote the event that the next customer fills his/her tank. Are events G and F independent ? Provide justification for your answer.
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