Math Is Fun Forum

lisathedork

Member

Registered: 2013-10-24

Posts: 36

Geometric Probability

The diameter of the black circle is 4 inches. The radius of the white middle circle is 6 inches and the Radius of the red circle is 9 inches.

1.    Robin knowns that if he hits the white part of the target, he just slightly win, therefore not embarrassing John. What is the probability that Robin will hit the white part of the target (not the red and not the bull’s-eye)? Show your work.

3.14(2)2
= 12.56

3.14(6)2
= 113.04

3.14(9)2
= 254.34

2.    After Robin shoots into the white area, John knows he cannot win, so he decides to set his sights on second place. To get second place, he needs to hit either the white circle or the bull’s-eye. What is the probability that he can do that? Show your work.

3.14(2)2 = 12.56 // 3.14(6)2 = 113.04 // 3.14(9)2 = 254.34

The table is 30 inches wide and 180 inches long. The width of the 2 and 3 rectangles is 12 inches. The sides of the 4 rectangle are 15 inches and the top and bottom are 12 inches. The 1 rectangle is twice as wide as the 2

3.    What are the dimensions of the 1 rectangle?
The dimensions of the 1 rectangle is

4.    What are the measurements of one of the 5 rectangles?
5.    You are playing shuffleboard in P.E. class. To score points, your disc must land in a box on the other side of the table and you are awarded the number of points that is in that box. What is the probability of scoring 1 point?
6.    What is the probability of scoring 2 points?
7.    What is the probability of scoring 3 points?
8.    What is the probability of scoring 4 point?
9.    What is the probability of scoring 5 point?
10.     What is the probability of scoring at all (any number of points)?

May I please get any helpful information on these problems? Anything is helpful.

Last edited by lisathedork (2015-09-05 08:28:28)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Geometric Probability

hi Lisa,

You have worked out the areas of the three circles.  Good start.

But what about probabilities ?

We are not told that Robin can even hit the target at all.  Maybe the chance that he will miss completely is 9/10 , say.

But without that information, I guess we are supposed to assume that he does hit the target somewhere and that the place he hits is proportional to the area of the region. (In reality players would like to think that they have a better chance of hitting close to the centre rather than just a random place on the target.  Whatever does  the questioner think they are doing?  This is a poor use of mathematical modelling.  More from my least favourite on-line course I suppose.)

So if black-area, white-area and red-area are the three areas you have calculated, my assumption means his hit is inside the  red-circle for certain and then we must compute the chance it is in white but not black.  My calculation would then be

Prob. = (white-area - black-area)/red-area

For the second part you can construct a similar calculation.  Note:  to be a probability it must be a number in the range 0 - 1.

I have added

[img]...[/img]

to your post so the diagram appears in the post.

I am not entirely sure about the measurements but I'm assuming (across measurement  then up measurement) that

rect-1 = 24 x 30

rect-2 = 12 x 30 = rect-3

rect-4 = 12 x 15 (but have I got these the right way round?)

rect-5 = 12 x 7.5 (assuming each 5 is the same)

Again you cannot do this question unless you assume that the player always gets somewhere in the play area and that the player hits an area at random rather than showing any skill at targeting.

So do the same as in the other questions.  Work out the relevant areas putting the target-area over 30 x 180 to get the probability.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob