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Q.

A PQRS square of side 5 cm is drawn in the interior of another square ABCD of side 10 cm and shaded as shown in the following figure. A point is selected at random from the interior of the square ABCD. What is the probability that the point will be chosen from the shaded part?

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a

16

b

120

c

38

d

14

answer is D.

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Detailed Solution

Given, a square of side 5 cm is drawn in the interior of another square of side 10 cm and shaded as shown in the following figure. A point is selected at random from the interior of the square ABCD.
The probability of an event to be occurred is the division of the number of favourable outcomes by the total number of outcomes that is,

Probability of an cvent = Number of favourable outcomes Total number of outcomes

Area of a square is (side)

2

.
Length of the sides of the square ABCD,

A B = B C = C D = D A = 10 cm

Also, the length of the square PQRS,

P Q = Q R = R S = S P = 5 cm

Find the area of the square ABCD by using the formula of area of a square that is, (side)

2

Area = (A B) 2 = (10) 2 cm 2 = 100 cm 2

Find the area of the square PQRS by using the formula of area of a square that is, (side)

2

Area = (P Q) 2 = (5) 2 cm 2 = 25 cm 2

Find the required probability by dividing the area of the square PQRS by the area of the square ABCD.

Probability = Area of the square P Q R S Area of the square A B C D = 125 cm 2 400 cm 2 = 14

The probability that the point will be chosen from the shaded part is

14

.
Hence the correct option is 4.

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