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What is the approximate probability thata point chosen inside the rectangle is inthe shaded region?

What is the approximate probability thata point chosen inside the rectangle is inthe-example-1
User Yasuhiro TATSUNO
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1 Answer

15 votes
15 votes

In order to determine the required probability, calculate the total area of the shaded regions frist:

Consider that there is a rectangle and a triangle with shaded area, then, you have:

A1 = (1 ft)(2 ft) = 2 ft² rectangle area

A2 = (2 ft)(2 ft)/2 = 2ft² triangle area

Then, the total shaded area is:

A = A1 + A2

A = 2 ft² + 2 ft²

A = 4 ft²

Next, calculate the total area of the given figure:

A' = (3 ft + 1 ft)(2 ft) = 8 ft²

Next, the probability is the quotient in between the area of th shaded regions over the area of the total figure:

p = A/A'

p = (2 ft²)/(4 ft²)

p = 0.50

Hence, the probability that a point chosen is inside a shaded region is 0.50

User Ben Glasser
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