How to solve this probability question!?

Question

There are 10 people, 6 of which have brown eyes. What is the chance that if you take 2 people out of that group that NEITHER of them will have brown eyes?

Is it, 40% X 3/9 = .133%??? That's the best I could come up with!

Also, what about this one?! What is the measure of one of the large angles of a parallelogram with vertices at (2,1) (6,5) (3,5) and (5,1)? I have no idea how to solve that!

Answer 1

There are at least two ways to do this one. A combinitoric method and a probability method (you have the correct answer btw):

There are C(10,2) = 45 possible sets of two people out of the group.
There are 4 people which do not have brown eyes.
Therefore, there are C(4,2) = 6 possible sets of two people neither of which have brown eyes.
6/45 = 2/15

Or... you can do it this way:
4/10 probability for the first person not to have brown eyes.
3/9 probability for the second person (there are 3 people left without brown eyes, and there are 9 people left altogether.)
4/10 * 3/9 = 12/90 = 2/15

C(a,b) = a!/[(a-b)!b!]

For your follow -up, see:

http://www.mudandmuck.com/str2/parallel.jpg

Answer 2

There are 4*3 ways to select 2 blue eyed people. there are 10*9 ways to select 2 people.
So, 12/90 = 2/15


Also, what about this one?! What is the measure of one of the large angles of a parallelogram with vertices at (2,1) (6,5) (3,5) and (5,1)? I have no idea how to solve that!

First sketch the parallelogram. You can see that it would help to move 2 units left and 1 unit down. So the new coordinates will be (0, 0), (4, 4), (1, 4), and (3, 0). The small angle now has tangent = 4/1, and the large angle = 180 degrees - the small angle (or pi - small angle in radians).

Answer 3

For your 2nd question, the bottom of the parallelogram is parallel to the x-axis. From the bottom right corner (5,1) to the top right corner (6,5) you have rise of 4, run of 1. so the 4/1 is the tangent of the exterior angle at that corner, 75.96°. Its supplement, 104.04°, is the large angle in the parallelogram.

Answer 4

6 people with brown eyes and 4 people with none.

The probability of picking a person that has no brown eye is 4/10. After one person is select, there are only 3 persons have no brown eyes out of 9. So the probability of pick the second person that has no brown eyes is 3/9

So, the probability of picking two persons that have no brown eyes is:

p = (4/10) * (3/9) = 2/15

Answer 5

Okay, I got the first one.
(4 x3)/(10 x 9) = 13.3%
There are 12 possible ways to get 2 people w/o brown eyes and you divide that by the 90 total possible combinations. It equals .1333333, or 13.3 %

Answer 6

Since you already have good answers for the first one, I'll do the second one.

The parallelogram has two sides parallel to the x axis, and two sides parallel to the vector (3,5)-(2,1) = (1,4)
This vector makes an angle arctan(4) with the horizontal
= 75.96 degrees.
This is the small angle.
The large angle is 180 - 75.96 = 104.04 degrees