A bag contains five sticks. The length of the sticks are 1 inches, 3 inches, 5 inches, 7 inches, and 9 inches. Suppose you pick 3 sticks from the bag at random.

Question

Its for my geometry class and I know that you can make a triangle if you draw any three sticks excluding the 1 inch stick  but I don't know how to calculate the probability.

Answer 1

Hi Zi,

 

There are 10 possible combinations of sticks that can be drawn from a group of 5 sticks

 

₅C₃ = (5*4*3)/(3*2)

 

= 10

 

and we can list those ten

 

1,3,5

1,3,7

1,3,9

1,5,7

1,5,9

1,7,9

3,5,7

3,5,9

3,7,9

5,7,9

 

to make a triangle,  the sum of any two sides must be greater than the third side

 

so if we look at the possible combinations there are only three cases where that is true

 

so our probablity fo drawing three sticks that would make a triangle is 3/10 or 30%

 

Hope this helps