5. Two fair, distinct dice (one red and one green) are rolled. Let A be the even
ID: 3277366 • Letter: 5
Question
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 of the 107th Congress is a Democratic senator. probability that a randomly selected member 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
5) here probability that red die shows even number P(A)=1/2 (as there are 3 even out of 6)_
probability that sum is even on two dies =P(B) =18/36 =1/2(as there are 18 even and 18 odd sum)
probability that even on red and sum is even =P(AnB) =9/36 ( there are 9 events where sum is even as well red die is even)
hence P(AnB)=P(A)*P(B)
therefore A and B are independent
6)
probability(democratic senator) =P( senator )*P( democrat|senator) =0.187*0.5=0.0935
7) proportion of US adults believe in AAlien =women and believe in alien +men and believe in alien
=0.52*0.33+(1-0.52)*0.54=0.4308 ~ 43.08%
8)P( smokes|lung disease ) =0.90
P( smokes and lung disease)=0.90*0.07 =0.063
also
P( smokes| not having lung disease ) =0.20
P( smokes and not having lung disease)=0.20*(1-0.07) =0.186
therfore P(Smokes) =( smokes and lung disease)+P( smokes and not having lung disease) =0.063+0.186=0.249
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