Understanding Probability: Quiz 4 Rubric for STAT 1053
School
George Washington University**We aren't endorsed by this school
Course
STAT 1053
Subject
Statistics
Date
Dec 12, 2024
Pages
2
Uploaded by UltraFlower13368
Rubric for STAT 1053 Quiz 4:Total points: 20 pointsQuestion 1 (6 points):GivenP(A) = 0.6andP(A∩B) = 0.18, andAandBare independent. CalculateP(A∪B).•Understanding Independence (2 points):The student should recognize that for inde-pendent events:P(A∩B) =P(A)·P(B)Hence, solve forP(B):P(B) =P(A∩B)P(A)=0.180.6= 0.3•Apply the Union Formula (3 points):Use the correct formula for the union of two events:P(A∪B) =P(A) +P(B)−P(A∩B)P(A∪B) = 0.6 + 0.3−0.18 = 0.72•Final Answer (1 point):Provide the final answer:P(A∪B) = 0.72Sample Answer:P(A) = 0.6,P(B) = 0.3P(A∪B) = 0.6 + 0.3−0.18 = 0.72Question 2 (6 points):SupposeP(A)>0andP(B)>0, andAandBare mutually exclusive (i.e. two eventscan not happen simultaneously). CanAandBbe independent? Justify your answer.•Definition of Mutually Exclusive Events (2 points):Clearly state that mutually ex-clusive events cannot occur at the same time, i.e.,P(A∩B) = 0.•Definition of Independent Events (2 points):Recognize that for independent events,P(A∩B) =P(A)·P(B).•Conclusion with Justification (2 points):Conclude that mutually exclusive events can-not be independent becauseP(A∩B) = 0, butP(A)·P(B)>0 when both probabilities arepositive. Therefore, the two cannot be independent.Sample Answer: Mutually exclusive events meanP(A∩B) = 0. For independent events,P(A∩B) =P(A)·P(B). SinceP(A)>0 andP(B)>0, mutually exclusive events cannot be independent.Therefore, they cannot be independent.1
Question 3 (8 points):Consider the following 2x2 table. FindP(Math|Stat)andP(Stat|Mathc).MathMathcTotalStat27342315Statc21168189Total294210504Math: students who like math;Stat: students who like statistics.•Conditional Probability forP(Math|Stat)(4 points):Apply the formula for conditionalprobability:P(Math|Stat) =P(Math∩Stat)P(Stat)From the table:P(Math|Stat) =273315= 0.866•Conditional Probability forP(Stat|Mathc)(4 points):Apply the formula:P(Stat|Mathc) =P(Stat∩Mathc)P(Mathc)From the table:P(Stat|Mathc) =42210= 0.2Sample Answer:P(Math|Stat) =273315= 0.866P(Stat|Mathc) =42210= 0.22