Question

find the probability that a point chosen randomly inside the rectangle is in each given shape. Round answers to the nearest hundreth. I need the percent.

Answer 1

A) 20.93%
B) 20%
C) 59.07%

Explanation
A) The total area of the rectangle is 6(10) = 60 ft². The area of the circle is 3.14(2²) = 12.56. This makes the probability of hitting the circle is 12.56/60 = 20.93%.

B) The total area of the rectangle is 60. The area of the trapezoid is 1/2(2+4)(4) = 12 ft². This makes the probability of hitting the trapezoid 12/60 = 20%.

C) The areas of the circle and trapezoid together are 12+12.56 = 24.56. This makes the rest of the area 60-24.56 = 35.44. This gives us the probability of not hitting the circle or trapezoid 35.44/60 = 59.07%

Answer 2

9) 20.93%

10) 20%

11) 40.93%

12) 59.07%

Explanation:

We are given a rectangle of dimensions 10ft×6ft which inscribes:

1. a circle of radius 2ft .
2. a trapezoid with two bases of length 4ft. and 2ft. and height 4ft.

Hence,

• Area of the circle is: πr² where r is the radius of circle.

Here we have: r= 2ft.

Hence, Area of circle=(3.14)×(2)²

= 12.56 square ft.

• Area of trapezoid is: 1/2×(sum of bases)×Height

=1/2×(4+2)×4

= 12 square ft.

• Similarly, Area of rectangle is: Length×Breadth

= 10×6

= 60 square ft.

Ques 9)

Probability that a point chosen lie on circle is:

Area of circle/Area of rectangle

= 12.56/60

= 0.2093333

In percent it is given by: 20.93%

Ques 10)

Probability that a point chosen lie on trapezoid is:

Area of trapezoid/Area of rectangle

= 12/60

= 0.2

In percent it is given by: 20%

Ques 11)

The circle or trapezoid is:

Probability that a point is chosen on circle+Probability that it is chosen on trapezoid.

= 40.93%

( Since,

P(A∪B)=P(A)+P(B)-P(A∩B)

and as circle and trapezoid do not have anything in common.

Hence, A∩B=∅

Hence, P(A∩B)=∅

Hence, P(A∪B)=P(A)+P(B) )

Ques 12)

Not the circle and the trapezoid this means that the point will lie in the shaded region.

Hence, Probability is:

100%-Probability(it will lie either on circle or trapezoid)

=100%-40.93%

=59.07%