+0  
 
0
143
1
avatar

A bag contains some sticks with lengths three feet, four feet, five feet, six feet, and seven feet.  Three sticks are chosen at random.

a) What is the probability that a triangle can be formed with the three chosen sticks?

b) What is the probability a right triangle can be formed with the three sticks?

Guest Feb 3, 2018
 #1
avatar+93618 
+2

A bag contains some sticks with lengths three feet, four feet, five feet, six feet, and seven feet.  Three sticks are chosen at random.

a) What is the probability that a triangle can be formed with the three chosen sticks?

 

3,4,5,6,7   there are 5C3 ways to chose three different ones  5C3=10  that is not many

If 3 are the same then there are 5*4C2 ways = 30 ways      

If they are all the same then there are 5 ways 

There are 45 ways to chose the 3 sticks

 

Also the sticks will from a triangle is the sum of the 2 little ones is longer than the big one. 

So

3,3,6

3,3,7

3,4,7 

are the only three selections that will not form a triangle

 

So

P(a triangle can be formed)= 42/45

 

b) What is the probability a right triangle can be formed with the three sticks?

 

The three sticks will from a right angle if the lengths of the sides are a pythagorean triad.  3,4,5 is the only one. 

 

so

P(forming a right angled triangle) = 1/45

 

P(forming a right angled triangle given that a triangle is able to be formed) = 1/42

Melody  Feb 3, 2018

9 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.