Geometric Probability Worksheet

**Page 1**

1.

Bus #R5711 runs every 35 minutes to Sam's college. If he arrives at the bus stop at a random time, then what is the probability that he will have to wait for 15 minutes or more? Assume that the bus stops for 5 minutes at the stop.

a. | $\frac{3}{4}$ | ||

b. | $\frac{5}{7}$ | ||

c. | $\frac{3}{8}$ | ||

d. | $\frac{5}{8}$ |

GH represents the time duration for which the bus waits at the stop.

If Sam arrives at the instant O, he has to wait for 40 minutes.

If Sam arrives at the instant E, he has to wait for 15 minutes.

The occurrence of the event of Sam waiting for 15 minutes or more is represented by OE.

Probability of Sam waiting for 15 minutes or more =

[From figure.]

Correct answer : (4)

2.

A dartboard is shown in the figure. Find the probability of hitting the shaded region. Given $a$ = 4 units, $b$ = 16 units. [π = 3]

a. | $\frac{1}{194}$ | ||

b. | $\frac{1}{192}$ | ||

c. | $\frac{1}{193}$ | ||

d. | $\frac{1}{191}$ |

Probability of hitting the shaded region =

Area of the shaded region = 4

[Area of square - Area of 2 semi circles.]

Area of the board = π × 16

Probability of dart hitting the target =

Correct answer : (2)

3.

Which of the following geometric probabilities is impossible?

a. | 0.45 | ||

b. | 1.20 | ||

c. | 0.00 | ||

d. | 1.00 |

Correct answer : (2)

4.

What is the probability of getting 75 points when the spinner is spun?

a. | $\frac{1}{3}$ | ||

b. | 1 | ||

c. | $\frac{5}{18}$ | ||

d. | $\frac{2}{9}$ |

P (getting 75 points) =

[Substitute.]

P(getting 75 points) =

[Simplify.]

Correct answer : (3)

5.

A dart thrown at a rectangular board ABCD is equally likely to land on any point. Find the probability of the dart hitting the inner rectangle PQRS. [Given $a$ = 21 cm, $b$ = 16 cm, $c$ = 18 cm, $d$ = 10 cm.]

a. | $\frac{29}{15}$ | ||

b. | $\frac{15}{28}$ | ||

c. | $\frac{4}{7}$ | ||

d. | $\frac{28}{15}$ |

[Area of rectangle = length × breadth.]

Area of the rectangle PQRS = PQ × QR = 18 × 10 = 180 cm

[Area of the rectangle = Length × breadth.]

P (Dart hitting the rectangle PQRS) =

The probability of the dart hitting the inner rectangle PQRS =

Correct answer : (2)

6.

A dart thrown at a line segment $\stackrel{\u203e}{\mathrm{AC}}$ can land at any point on it. What is the probability that it lands on $\stackrel{\u203e}{\mathrm{BC}}$? [Given $a$ = 19, $b$ = 9.]

a. | $\frac{5}{14}$ | ||

b. | $\frac{9}{19}$ | ||

c. | $\frac{9}{28}$ | ||

d. | $\frac{9}{29}$ |

P (Dart landing on

[Substitute and simplify.]

Correct answer : (3)

7.

A dart is thrown at a board in the form of a circle. If the dart hits the board, then what is the probability that it will land in the shaded area? [Given $x$° = 66^{o}.]

a. | $\frac{49}{60}$ | ||

b. | $\frac{37}{45}$ | ||

c. | $\frac{149}{180}$ | ||

d. | $\frac{73}{90}$ |

Required probability =

Required probability =

[Area is proportional to the central angle.]

Required probability =

[Substitute and simplify.]

Correct answer : (1)

8.

Equilateral triangle PQR, of side 36 in. is inside a square ABCD of side 48 in.. A dart is thrown at the square board. If the dart lands on the board and that it is equally likely to land on any point, then the probability of hitting the triangle PQR is

a. | $\frac{9\sqrt{3}}{64}$ | ||

b. | $\frac{18\sqrt{3}}{64}$ | ||

c. | $\frac{11\sqrt{3}}{64}$ | ||

d. | $\frac{9}{64}$ |

[Area of a square = (side)

Area of the ΔPQR =

[Area of an equilateral triangle =

P(Dart hitting ΔPQR) =

Required probability =

[Substitute and simplify.]

Correct answer : (1)

9.

A dart is thrown at a square ABCD. What is the probability that it lands in the shaded region?

a. | $\frac{2}{5}$ | ||

b. | $\frac{1}{5}$ | ||

c. | $\frac{1}{4}$ | ||

d. | $\frac{1}{3}$ |

P (Dart landing in the shaded portion AOB) =

Required probability =

Correct answer : (3)

10.

A dart is thrown at ΔABC. What is the probability that it lands on shaded portion MNK?

a. | $\frac{1}{8}$ | ||

b. | $\frac{1}{32}$ | ||

c. | $\frac{1}{16}$ | ||

d. | $\frac{1}{24}$ |

[By symmetry.]

Area of ΔMNK =

[By symmetry.]

Area of ΔMNK =

[Step1 and Step2.]

[Step3.]

P (Dart landing on shaded portion MNK) =

[Step 4.]

Correct answer : (3)