Solution:
we are given that
Sandy and Robert each have various polygons in their polygon buckets. Sandy randomly selects a polygon from her polygon bucket and Robert randomly selects a polygon from his.
A. who has a greater probability of selecting a quadrilateral? Justify your conclusion.
Answer: Sandy has greater proabaility(1/2) because in sandy bucket number of Quadrilaterals are more than the Robert(1/5). Also the number of polygon is less in case of Sandy. Hence greater proabaility for Sandy.
B. who has a greater probability of selecting an equilateral polygon? justify your conclusion.
Answer: Aagain sandy has greater probability because for sandy its 1/4 and for Robert its 1/5.
C. what is more likely to happen: Sandy selecting a polygon with at least two sides that are parallel or Robert selecting a polygon with at least two sides that are equal ?
Answer: Sandy has the probability of [tex] \frac{2}{4}=\frac{1}{2} [/tex], while RFobert has the probability of [tex] \frac{1}{5} [/tex]. So again sany has greater probability.
Answer:
(A)
Number of Quadrilateral in Sandy Bucket =[Square,Rhombus]=2
Number of Quadrilateral in Robert Bucket =[Kite,Quadrilateral]=2
Probability of an event
[tex]=\frac{\text{Total Favorable Outcome}}{\text{Total Possible Outcome}}[/tex]
→Probability of Selecting a Quadrilateral by Sandy
[tex]=\frac{2}{4}\\\\=0.50[/tex]
→Probability of Selecting a Quadrilateral by Robert
[tex]=\frac{2}{5}\\\\=0.40[/tex]
Selecting a Quadrilateral by Sandy has more probability than Selecting a Quadrilateral by Robert.
(B)
Number of equilateral polygon in Sandy's Bag={Square, Equilateral Triangle,Regular Hexagon}
Probability of selecting an equilateral polygon by Sandy
[tex]=\frac{3}{4}\\\\=0.75[/tex]
Number of equilateral polygon in Robert's Bag=0
Probability of selecting an equilateral polygon by Robert=0
So, Probability of selecting an equilateral polygon by Sandy is greater than selecting an equilateral polygon by Robert.
(C)
Selecting a polygon with at least two sides that are parallel
={Square, Rhombus,Regular Hexagon}
Selecting a polygon with at least two sides that are equal
={Isosceles Triangle, Right Isosceles Triangle,Kite}
Probability of Selecting a polygon with at least two sides that are parallel out of four geometrical shapes by Sandy
[tex]=\frac{3}{4}\\\\=0.75[/tex]
Probability of Selecting a polygon with at least two sides that are parallel out of four geometrical shapes by Robert
[tex]=\frac{3}{5}\\\\=0.6[/tex]
Selecting a polygon with at least two sides that are parallel by Sandy is more likely than Selecting a polygon with at least two sides that are equal by Robert.
