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?
A) 1/26
B) 3/52
C) 6/169
D) 9/169

Answer 1

The right answer is A option.

Answer 2

Answer:

$\frac{1}{26}$

Step-by-step explanation:

Given : Kyle has three short straws, four medium straws, and six long straws.

To Find: . If he randomly draws two straws, one at a time without replacement, what is the probability that both are short straws?

Solution:

Short Straws = 3

Medium Straws = 4

Long Straws = 6

Total straws = 3+4+6=13

Now , Probability of getting short straw on first draw = $\frac{\text{No. of short straws}}{\text{Total Number of straws}}$

                                                                                      = $\frac{3}{13}$  

Now the straw is not replaced .

So, Total no. of straws = 12

No. of short straws = 2

Now probability of getting short straw on Second draw = $\frac{\text{No. of short straws}}{\text{Total Number of straws}}$

                                                                                      = $\frac{2}{12}$  

Now ,the probability that both are short straws = $\frac{2}{12} \times \frac{3}{13}$  

                                                                               = $\frac{6}{156}$  

                                                                               = $\frac{1}{26}$  

Thus Option A is correct.

Hence ,the probability that both are short straws is  $\frac{1}{26}$ .