Geometrical Probability

Q.

A missing helicopter is reported to have crashed somewhere in the rectangular region shown below. Find the probability of it crashing in the lake.

1. $\frac{4}{29}$
2. $0$
3. $\frac{3}{28}$
4. $\frac{5}{27}$

Q.

Question 2

3 × 10000 + 7 × 1000 + 9 × 100 + 0 ×10 + 4 is the same as:

(A) 3794
(B) 37940
(C) 37904
(D) 379409

Q.

Indians, Egyptians, Europeans and Australians reside in a village of area 200$k{m}^2$. If the area is equally divided among the four civilizations, what is the probability that a particular person lands on the land occupied by Indians or Europeans?

1. 

2. 

3. 

4. 

Q.

If given a dart board of radius 50 cm. What is the probability that you hit the bull's eye of radius 5 cm?

1. 1

2. $\frac{1}{1000}$

3. $\frac{1}{100}$

4. $\frac{1}{10}$

Q.

Question 42

0.5 ___ 0.7 = 0.35

Q.

In a circular dartboard of radius 25cm, there are 5 concentric circles. the radius of each inner concentric circle is 5 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. $\frac{1}{\pi }$

2. 1

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

4. $\frac{1}{25}$

Q. A bag contains 4 black, 6 white and 8 red balls. One ball is drawn at random from the bag. Find the probability that the ball drawn is:
i) white
ii) not red
iii) red or white
iv) red and white
v) neither black nor white
vi) either red or black
[6 MARKS]

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. 0.60

2. 0.33

3. 0.45

4. 0.50

Q.

Given above is a figure of a dartboard, where the length and the breadth of the rectangle are respectively 7 feet and 6 feet, and the radius of the circle is 2 feet. The probability that a point chosen from the given figure lies inside the circle is:

1. $\frac{\pi }{42}$

2. $\frac{4\pi }{21}$

3. $\frac{2\pi }{21}$

4. $\frac{\pi }{21}$

Q. Given a dart board of radius 50 cm, the probabilityof hitting the bull's eye of radius 5 cm is .

1. 1
2. 0.1
3. 0.01
4. 0.2

Q. Given a dart board of radius R cm, the probability that you hit the bull's eye of radius r cm is .

1. $\frac{R}{r}$
2. $\frac{r}{R}$
3. r2R2

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. 0.60

2. 0.33

3. 0.45

4. 0.50

Q.

In a circular dartboard of radius 20 cm, there are 5 concentric circles. The radius of each successive inner concentric circle is 4 cm less than the preceding the outer concentric circle. What is the probability that the dart hits the smallest circle?

1. 

2. 

3. 

4. 0

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

1. 
2. 
3. 

Q.

Indians , Egyptians , Europeans and Australians are resided in a village of area 200$k{m}^2$. If the area is equally divided among the four civilizations, what is the probability that a particular person lands on the land occupied by Indians or Europeans?

1. 

2. 

3. 

4. 

Q.

What is the probability that you land on the land occupied by Indians or Europeans or Egyptians, if Indians , Egyptians , Europeans and Australians resided in a village of area 100$k{m}^2$ which is equally divided among the four civilizations?

1. 1.00

2. 0.75

3. 0.50

4. 0.25

Q. If the radius of outer circle is x times radius of inner circle, then the probability that a dart hits the inner circle is $\frac{1}{x^2}$

1. True
2. False

Q.

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

1. $0$

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

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

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

Q.

Write the predecessor and successor of $997$.

Q. A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 and these are equally likely outcomes. What is the probability that it will point at:

(ii) an odd number.

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. $\frac{1}{5}$

2. $\frac{1}{25}$

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

4. 0

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

1. 
2. 
3. 

Q. The Probability distribution of $X$, the number of defects per $10$ meters of a fabric is given by

$x$	$0$	$1$	$2$	$3$	$4$
$P(X=x)$	$0.45$	$0.35$	$0.15$	$0.03$	$0.02$

Find the variance of $X$.

Q. A chopper was found missing allegedly in the area shown below:
What is the probability it crashed into the lake?

1. 0.25
2. 0.185
3. 0.352
4. 0.5

Q. There is a circle with inner radius of 4 cm and outer radius of 6 cm. A coin is tossed onto this circle. What is the probability of the coin falling outside the smaller circle but inside the bigger circle?

1. $\frac{2}{3}$
2. $\frac{4}{9}$
3. $\frac{5}{9}$
4. $\frac{7}{9}$

Q. Difference between mean and variance of a Binomial variate is ${}^{\prime }{1}^{\prime }$ and difference between their squares is ${}^{\prime }{11}^{\prime }.$ Find the probability of getting exactly three success

Q. A bag consists of 7 red balls, 9 white balls and 8 green balls. Three balls are taken out of the bag at random one-by-one. What is the probability that the third ball is neither green nor white if the first two balls are red?

Q. A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 and these are equally likely outcomes. What is the probability that it will point at:

(iii) a number greater than 2

Q. A missing helicopter is reported to have crashed somewhere in the rectangular region shown below. Find the probability of it crashing in the lake.

1. $\frac{4}{29}$
2. 0
3. $\frac{3}{28}$
4. $\frac{5}{27}$

Q. $10p+10=100$