PLEASE SHOW WORK!! THANKS!! 5. Two fair, distinct dice (one red and one green) a

Question

PLEASE SHOW WORK!! THANKS!!

5. Two fair, distinct dice (one red and one green) are rolled. Let A be the event the red die comes up even and B be the event the sum on the two dice is even. Are A, B independent events? 6. For the 107th Congress, 18.7% of the members were senators and 50% of the senators were Democrats. Using the multiplication rule, determine the probability that a randomly selected member of the 107th Congress is a Democratic senator. 7. According to the Current Population Reports, 52% of U.S. adults are women. Opinion Dynamics Poll published in USA Today shows that 33% of U.S. women and 54% of U.S. men believe in aliens. what percentage of U.S. adults believe in aliens? 8, According to the American Lung Association 7% of the population has lung disease. Of the people having lung disease 90% are smokers. Of the people not having lung disease 20% are smokers. what are the chances that a smoker has lung disease?

Explanation / Answer

6. P(Senator) = 0.187

P(Democrats|Senator) = 0.50

Hence,

P(Democrat and senator) = P(Senator)*P(Democrats|Senator) = 0.187*0.5 = 0.0935 i.e. 9.35%

7. P(Women) = 0.52

P(Men) = 1 - 0.52 = 0.48

P(Believe in Aliens|Men) = 0.54

P(Believe in Aliens|Women) = 0.33

Hence,

P(Believe in Aliens) = 0.48*0.54 + 0.52*0.33 = 0.4308

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