Geometric Probability

Q.

Three ships $A,B$ and $C$ sail from England to India. If the ratio of their arriving safely are $2:5$, $3:7$ and $6:11$ respectively then the probability of all the ships for arriving safely is

1. $\frac{18}{595}$

2. $\frac{6}{17}$

3. $\frac{3}{10}$

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

Q. A dart is thrown at a circular dartboard such that it will land randomly over the area of the dartboard. What is the probability that it lands closer to the center than to the edge?

1. 30%
2. 40%
3. 20%
4. 25%

Q. A dart is thrown and it hits the dartboard. The dart is equally likely to land on any point on the dart board. Find the probability that the dart lands in the red region. (The measurements are in inches).

1. 10%
2. 20%
3. 5%
4. 15%

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. 0

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

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

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

Q. The dart board is formed of concetric circles with radius 3 cm, 2 cm and 1 cm as shown in the figure below. What will be the probability of dart hitting the area A?

1. 53 %
2. 48 %
3. 60 %
4. 55.6 %

Q.
Given above is a figure of a dartboard, where the length and the breadth of the rectangle are respectively 3 feet and 2 feet, and the radius of the circle is 1 foot. What is the probability that a point chosen from the given figure lies inside the circle?

1. $\frac{2}{7}$
2. $\frac{\pi }{6}$
3. $\frac{\pi }{7}$
4. $\frac{1}{6}$

Q. If we select a letter from the word 'PROBABILITY' at random, what is the probability that it is a vowel?

1. $\frac{3}{11}$
2. $\frac{2}{11}$
3. $\frac{4}{11}$
4. $\frac{5}{11}$

Q.

$$\begin{array}{cc}TheWickerMan& 04:35\\ GhostoftheNavigator& 06:50\\ BraveNewWorld& 06:18\\ BloodBrothers& 07:14\\ TheMercenary& 04:42\\ DreamofMirrors& 09:21\\ TheFallenAngels& 04:00\\ TheNomad& 09:05\\ OutoftheSilentPlanet& 06:25\\ TheThinLineBetweenLove& 08:27\end{array}$$

Find the probability that a song will be (i) at least 7 minutes long (ii) less than 5 minutes long.

Q. You work for a temporary employment agency. You live on the west side of town and prefer to work there. The work assignments are spread evenly throughout the rectangular region shown. Find the probability that an assignment chosen at random for you is on the west side of town.

1. 25%
2. 28%
3. 30%
4. 20%

Q. You are visiting San Francisco and are taking a trolley ride to a store on Market Street. You are supposed to meet a friend at the store at 3:00 P.M. The trolleys run every 10 minutes and the trip to the store is 8 minutes. You arrive at the trolley stop at 2:48 P.M. What is the probability that you will arrive at the store by 3:00 P.M.?

1. 30%
2. 20%
3. 60%
4. 40%

Q. What will be the probability of a point chosen at random on $\overline{RS}$ is on $\overline{TU}$ ?

1. 35%
2. 40%
3. 20%
4. none of the above.