In each of three boxes are four straws with integer lengths cm, cm, cm, and cm. A straw is randomly selected from each box. What is the probability that a triangle can be formed with the three straws chosen?

Could anyone also add an explanation with their answer? Thanks!

moneydude242 Jul 13, 2023

#1**0 **

*Could anyone also add an explanation with their answer?*

The sum of any two sides of a triangle must be greater than its third side.

That's the explanation. The length of the straws wasn't visible in the post.

Bosco Jul 13, 2023

#3**0 **

OK corrected version:

In each of three boxes are four straws with integer lengths 1 cm, 2 cm, 3 cm, and 4 cm. A straw is randomly selected from each box. What is the probability that a triangle can be formed with the three straws chosen?

Could anyone also add an explanation with their answer? Thanks!

moneydude242 Jul 13, 2023

#4**0 **

Here is an explanation of the answer:

We can't form a triangle if any of the straws have length 1, so we need to consider the cases where all three straws have length 2, 2 and 3, or 3 and 4.

Case 1: All three straws have length 2. There are (34)=4 ways to choose which straws to select, so the probability of this case is 4/4^3=1/64

Case 2: Two straws have length 2 and one has length 3. There are (24)=6 ways to choose which straws to select, so the probability of this case is 6/4^3=3/64.

Case 3: One straw has length 2 and the other two have length 3. There are (14)=4 ways to choose which straw has length 2, so the probability of this case is 4/4^3=1/64.

The total probability is then 1/64+3/64+1/64=5/64.

Guest Jul 13, 2023