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

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 $\frac{3}{13}$.

After a short straw is drawn, there are two short straws and twelve total straws, a probability of $\frac{2}{12} = \frac{1}{6}$.

Thus, the probability of both of these events occurring is $\frac{3}{13} \cdot \frac{1}{6} = \boxed{\frac{1}{26}}$.

Answer 2

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 .