+0  
 
0
83
1
avatar

A bag contains some sticks with lengths three feet, four feet, five feet, six feet, seven feet, and eight 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?

 Nov 26, 2020
 #1
avatar+116126 
+1

C(6, 3)  = 30 possibilities

 

3  4  5  6  7  8 

Not all will  work......we must satisfy  the triangle inequality  that says  the sum of any two side lengths of a triangle  must exceed the length of the remaining  side

 

Possible lengths

 

3 - 4 - 5    3 - 5 - 6     3 - 6 - 7     3 - 7 - 8     4 - 5 - 6      4 - 6 - 7     4 - 7 - 8     5 - 6 - 7   

3 - 4 - 6    3 - 5 - 7     3 - 6 - 8                      4 - 5 - 7      4 - 6 - 8                       5 - 6 - 8 

                                                                    4 - 5 - 8

 

5 - 7 - 8       6 - 7 - 8

 

a)  Probability  is  17/30

 

b)  There is only 1 right triangle    3 - 4  - 5....probability is  1/30

 

 

cool cool cool

 Nov 26, 2020

81 Online Users

avatar
avatar
avatar