4 5 geometric probability
This presentation is the property of its rightful owner.
Sponsored Links
1 / 14

4.5: Geometric Probability PowerPoint PPT Presentation


  • 60 Views
  • Uploaded on
  • Presentation posted in: General

4.5: Geometric Probability. GSE’s Primary. p. 551-558. Primary GSE. M(DSP)–10–5 Solves problems involving experimental or theoretical probability. . Secondary GSE’s.

Download Presentation

4.5: Geometric Probability

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


4 5 geometric probability

4.5: Geometric Probability

GSE’s

Primary

p. 551-558

Primary GSE

M(DSP)–10–5 Solves problems involving experimental or theoretical probability.

Secondary GSE’s

M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses theorems to solve problems involving angles, lines, polygons, circles, or right triangle ratios (sine, cosine, tangent) within mathematics or across disciplines or contexts (e.g., Pythagorean Theorem, Triangle Inequality Theorem).

M(G&M)–10–6 Solves problems involving perimeter, circumference, or area

of two dimensional figures (including composite figures) or surface area

or volume of three


4 5 geometric probability

Probability=


Probability

Probability

  • Definition - a # from 0 to 1 that represents the chance that an event will occur.

  • 0 – no chance

  • 1 – 100% chance (the event will always occur).

  • .5 or ½ - 50% chance

.5

0

1

Could go either way

No chance

Def. gonna happen


4 5 geometric probability

  • Geometric Probability – probability

  • involving lengths or areas.


Length probability postulate

Length Probability Postulate

  • If a point on AB is chosen at random and C is between A and B, then the probability that the point is on AC is Length of AC

    Length of AB


Example

Example

Find the probability that a point chosen at random in AF is

also part of each of the segments


Area problems

Area Problems

  • If a point in a region A is chosen at random, then the probability that the point is in region B, which is in the interior region A, is Area of Region B

    Area of Region A

    *Note. Does not always have to be same shapes. Could be a circle inside a square, triangle inside a circle, etc. Remember the formulas.


Example1

Example

A common game is darts. What is the probability of randomly throwing a dart such that it hits within the red area, given that the dart will always land within the boundary of the outer circle?

  • P(Red)=

5

1


Problems

Problems

  • A dart is thrown at random onto a board that has the shape of a circle as shown below.

  • Calculate the probability that the dart will hit the shaded region. (Use π =3.14 )


4 5 geometric probability

If a dog had an accident in the house, what is the probability of it occurring in the bedroom ?


Problem

Problem

  • The figure shows a circle divided into sectors of different colors. If a point is selected at random in the circle, calculate the probability that it lies:

  • a) in the red sector.b) in the green sector.c) in the blue sector.

  • d) in any sector except the green sector.


4 5 geometric probability

Square ABCO contains part of a circle. What is the probability that a point

Chosen at random would be in the shaded part?


Problem1

An arrow is shot at random onto the rectangle PQRS. Calculate the probability that the arrow strikes:

a) triangle AQB.

b) a shaded region.

c) either triangle BRC or the unshaded region.

In the figure below, PQRS is a rectangle, and A, B, C, D are the midpoints of the respective sides as shown.

Problem


Homework

Homework


  • Login