Probability of Parallelogram, given opp. angles measure 120

[juvenilepunk]

I really need help with this question, I have to present the answer and how to do it in front of my class tomorrow. If someone can please help me with as much detail as possible I would really appreciate it.

Thanks.

 

[mmm4444bot]

Re: Probability of a Parallelogram



If you have a parallelogram where two opposite angles are fixed at 120 degrees, then how many possibilities are there for the measure of the other pair of angles?

How many multiples of ten are there from 10 through 80? (I'm guessing, here; I really don't know what probability they want.)

When did you get this assignment? What is your reasoning so far?

 

[chivox]

Re: Probability of a Parallelogram

Juvenilepunk, thanks for posting the image, because I wouldn't have believed this exercise if you had just typed it in. Nevertheless, you still have to do a presentation, right?

Basically, I do not understand the probability here. We're talking about an infinite number of possible quadrilaterals. Some of them have opposite angles of 60 degrees, and those would be parallelograms. However, you can also draw a quadrilateral with 120-degree opposite angles, with an 80-degree angle and a 40-degree angle. There are an infinite number of those as well. How about 110 and 10 being the other two angles? There's also an infinite number of those.

What I would recommend for your presentation: Cut out two templates at 120-degree angles. Move them all around on a plane as opposite angles of a quadrilateral, and see how many different figures you can get. Be sure to include not only the nice parallelograms, but also the irregular quadrilaterals, which are not parallelograms.

With infinity in the denominator in terms of the total number of possibilities (because of the side lengths), I'm not sure how to compute the probability. I know there's the same infinite number for all multiples of 10, but it's still infinity, and that just gives me a headache. Does infinity equal infinity? Or better, if two infinite sets are mutually exclusive, does each have a probability of 0.5? That question is not what we're trying to teach here, but that is how the writer has framed the problem. We need to stick to geometry. Good luck with your presentation, but I would recommend forgetting the probability part of the question and focus on discovering the many different ways you can arrange your templates.

As an aside, juvenilepunk, after you're done with your presentation, would you mind telling me who wrote this textbook? You can do so in a private message if you want. Thanks.

 

[wjm11]

If two opposite angles of a quadrilateral measure 120 and the measures of the other angles are multiples of 10, what is the probability that the quadrilateral is a parallelogram?

Two angles are 120. 360 – 2(120) = 120. The other angles, call them angle 1 and angle 2, must total 120 degrees.

Possible combinations of the other two angles:
Angle 1, angle 2:
10, 110
20, 100
30, 90
40, 80
50, 70
60, 60
70, 50
80, 40
90, 30
100, 20
110, 10

Only the “60 – 60” solution makes this a parallelogram. One solution out of 11 means the probability is 1/11.

Alternatively, if we count “mirror” solutions such as “80 – 40” and “40 – 80” only once, then we get a probability of 1/6.

Hope that helps.

 

[chivox]

Possible combinations of the other two angles:
Angle 1, angle 2:
10, 110 -- wjm: This represents an infinite number of quadrilaterals. Some are little, some big, some really big, some huge, since the lengths of the sides were not constrained in the idiotic formulation of the problem by this author.

Alternatively, if we count “mirror” solutions such as “80 – 40” and “40 – 80” only once, then we get a probability of 1/6.

Hope that helps.

... All the other so-called single events you identified also must represent an infinite number of possibilities, given the constraints of the problem. What would help this student is a good formulation of the problem. This is not "probability." Now, if we want to go around and teach people that "probability" is not very precise, fine. I can't argue that this is probably where education about mathematics is headed (if this textbook is any indication, anyway).

But the probability is the number of desirable outcomes (infinity, in our case) divided by the total number of outcomes, which, in our case, is

for 110, 10: infinity
for 100, 20: infinity
...

= six times infinity or 11 times infinity (you decide if we count the so-called "mirrors").

What is infinity divided by six or 11 times infinity? Of course, the limit goes to 1/6 or 1/11 as we approach infinity, and I'm sure this student's teacher said one of those was the "right" answer. I was simply trying to give an idea for making a presentation live in a math class, which is what he or she asked for help with in the first place.