Practice Quiz

SAT Math

Category - Stats and Probability

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In the figure below, ABCD is a square whose side is 4, and points E, F, G and H divide the corresponding sides of ABCD in a ratio 1:3.

What is the probability of selecting a point from the shaded region?
  1. 3/8
  2. 1/3
  3. 1/2
  4. 5/8
  5. 2/3
Explanation
Answer: D -The probability of selecting a point from the shaded region is 5/8. The shaded polygon is a square.

The side of the shaded square is: HG^2=DH^2+DG^2=1^2+3^2=1+9=10⟹HG=√10.
Probability=({area of shaded square})/({area of ABCD})=(√10)^2/4^2 =10/16=5/8
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