Question

Kyle has three short straws, four medium straws, and six long straws. If he randomly draws two straws, one at a time without replacement, what is the probability that both are short straws?

Answer 1

Answer: 1 /26

Step-by-step explanation: To calculate probability of two dependent events you multiply their probabilities together. Remember that without replacement means you have to subtract one from the denominator. Therefore you should multiply 3/ 13 ⋅ 2/ 12 to get the solution 1/ 26 .

Answer 2

Before the first straw is drawn, there are three short straws and
`3+4+6=13` straws in all. Thus, the probability of drawing a short straw first is
`(3)/(13)`.

After a short straw is drawn, there are two short straws and twelve total straws, a probability of
`(2)/(12) = (1)/(6)`.

Thus, the probability of both of these events occurring is
`(3)/(13) \cdot (1)/(6) = \boxed{(1)/(26)}`.