Question

A student has two straws. One is 5 cm long and the other is 8 cm long. He picks a third straw at random from a group of four straws whose lengths are 3 cm, 7 cm, 11 cm, and 13 cm. What is the probability that the straw he picks will allow him to form a triangle? Justify your answer

Answer 1

1/2.

Explanation:

There are 4 possible outcomes after picking the third straw:

Length of the straws:

5 8 3 cm

5 8 7 cm

5 8 11 cm

5 8 13 cm

To form a triangle the sum of any 2 sides must not be equal or less than the third side.

So the first set will not form a triangle because 3 + 5 = 8.

Second set: these can form a triangle.

Third set: also can form a triangle.

Fourth set: No because 5 + 8 = 13

So only 2 sets can form triangles.

So the probability = 2/4 = 1/2.