Geometric Probability

Q. Length and breadth of a rectangular garden are 77 m and 50 m. There is a circular lake in the garden having diameter 14 m. Due to wind, a towel from a terrace on a nearby building fell into the garden. Then find the probability of the event that it fell in the lake.

Q.

In a bag there are 44 identical cards with figure of circle or square on them. There are 24 circles, of which 9 arc blue and rest are green and 20 squares of which 11 are blue and rest are green. One card is drawn from the bag at random. Find the probability that it has the figure of (i) square (ii) green colour, (iii) blue circle and (iv) green square.

Q. The probability of a coin falling in the red region is 0.15.

1. True
2. False

Q.

Out of 50 students in a class taking a test, 35 of them passed whereas the other 15 failed. What is the probability that a student selected at random passed the test?

1. 0.15
2. 0.3
3. 0.35
4. 0.7

Q. Tap on the region in which the probability of finding a crashed plane is $\frac{1}{9}.$

1. 
2. 
3. 

Q.

Find the probability that a dart hits the region X(inner circle) if the radius of the outer circle is $x$ times radius of the inner circle (x>2).

1. $\frac{1}{x^2}$

2. $\frac{1}{x}$

3. 1

4. $\frac{1}{x^3}$

Q.

In a circular dartboard of radius 20 cm, there are 5 concentric circles. the radius of each inner concentric circle is 4 cm less than the outer concentric circle. Find the probability that a dart hits anywhere in the smallest circle assuming that the dart doesn't hit on the boundary of any circle.

1. 

2. 

3. 

4. 0

Q. An archer is getting ready to hit the bullseye of a target. What is the probability of him missing the bullseye, if he is certain to hit the target? The target is designed so that each concentric circle is 5 inches wide and the bullseye is a circle of radius 5 inches.

1. $\frac{1}{5}$
2. $\frac{2}{5}$
3. $\frac{24}{25}$
4. $\frac{25}{100}$

Q. The figure shows a circle with centre O and radius 4cm. $\angle$ BOD = ${72}^{\circ }$. A point is selected at random inside the circle. Find the probability that point lies inside the sector.

1. $\frac{3}{5}$
2. $\frac{2}{5}$
3. $\frac{4}{5}$
4. $\frac{1}{5}$

Q. Find the probability that a coin tossed falls in each of the shaded region. (all measures in cm)

1. 0.2
2. 0.25
3. 0.66

Q.

Indians , Egyptians , Europeans and Australians are residing in a village of area 200 $k{m}^2$. If the area is equally divided between the four countries, what is the probability that a particular person who lands in the village, finds himself in the area occupied by either Indians or Europeans?

1. 0.33

2. 0.60

3. 0.45

4. 0.50

Q.

Shooters are required to shoot at a target which is circular in shape. The target is fixed onto a rectangular board whose dimensions are $44cm\times 21cm$. Assuming that all the bullets hit the rectangular board, what is the probability that the bullets hit the circular target? (Given that: radius of the circle = 7 cms. )

1. $\frac{1}{2}$

2. $\frac{3}{7}$

3. $0$

4. $\frac{1}{6}$

Q.

Shooters are required to shoot at a target which is circular in shape. The target is fixed onto a rectangular board whose dimensions are $44cm\times 21cm$. Assuming that all the bullets hit the rectangular board, what is the probability that the bullets hit the circular target? (Given that: radius of the circle = 7 cms. )

1. $\frac{1}{2}$

2. $\frac{3}{7}$

3. $\frac{1}{6}$

4. $0$

Q.

You are given a dart board of radius R cm. What is the probability that you hit the bull's eye of radius r cm?

1. $\frac{r^2}{R^2}$

2. $\frac{R}{r}$

3. $\frac{r}{R}$

4. 1

Q. Find the probability that a coin tossed falls in each of the shaded region. (all measures in cm)

1. 0.66
2. 0.25
3. 0.2

Q.

a circular target of radius 11 cm consists of an inner circleof radius 5 cm and three concentric circles of radii 7cm, 9cm and 10 cm dividing the target into four regions. If a shot hit the target find the probability of hitting each region. If you shoot target 121 times, what is your expectation? How can you improve your performance?

Q. An archer is getting ready to hit the bullseye of a target. What is the probability of him missing the bullseye, if he is certain to hit the target? The target is designed so that each concentric circle is 5 inches wide and the bullseye is a circle of radius 5 inches.

1. $\frac{1}{5}$
2. $\frac{2}{5}$
3. $\frac{24}{25}$
4. $\frac{25}{100}$

Q. The figure shows a circle with centre O and radius 4cm. $\angle$ BOD = ${72}^{\circ }$. A point is selected at random inside the circle. Find the probability that point lies inside the sector.

1. $\frac{3}{5}$
2. $\frac{2}{5}$
3. $\frac{4}{5}$
4. $\frac{1}{5}$

Q. The figure shows a circle with centre O and radius 4cm. \(\angle\) BOD = \(72^\circ\). A point is selected at random inside the circle. Find the probability that point lies inside the sector.