1. Two fair, distinct dice are rolled. What is the probability that the first di
ID: 3276801 • Letter: 1
Question
1. Two fair, distinct dice are rolled. What is the probability that the first dice comes up 1 given that the sum on the two dice is 5? Use this information for problems 2, 3, and 4: The following data on the marital status of 1000 U.S. adults was found in Current Population Reports: Single Married Widowed Divorced M- Male 129298 13 40 Female 104 305 57 54 S. 2. (a) Find P(M2 (b) Find P(Si) (c) Find P(M4nS.) (d) Interpret your answers to (a), (b), and (c) Find P(Ma|S) Find P(S2M4) Interpret your answers to (a) and (b) 4. Are M1 and S independent events? Justify your answer 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 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
Ans:
1)
A=first dice comes up with 1={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)}
A and B=favourable outcomes for sum of 5 and first dice comes up with 1={(1,4)}
B=favourable outcomes for sum of 5 ={(1,4),(2,3),(3,2),(4,1)}
P(A/B)=P(A and B)/P(B)=(1/36)/(4/36)=1/4
2)Calculate joint probability distribution dividing each entry by 1000
a)P(M2)=0.298+0.305=0.603
b)P(S1)=0.129+0.298+0.013+0.04=0.48
c)P(M4 and S2)=0.054
a) and b) are marginal probabilities and c) is joint probability.
3)P(M3/S1)=P(M3 and S1)/P(S1)=0.013/0.48=0.0271
P(S2/M4)=P(S2 and M4)/P(M4)=0.054/0.094=0.5745
4)P(M1 and S1)=0.129
P(M1)*P(S1)=0.233*0.48=0.112
As,P(M1 and S1) is not equal to P(M1)*P(S1),hence M1 and S1 are not independent events.
M1 M2 M3 M4 Total S1 129 298 13 40 480 S2 104 305 57 54 520 Total= 233 603 70 94 1000 M1 M2 M3 M4 Total S1 0.129 0.298 0.013 0.04 0.48 S2 0.104 0.305 0.057 0.054 0.52 Total= 0.233 0.603 0.07 0.094 1Related Questions
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