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

`(1)/(26)`

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}}`

=
`(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}}`

=
`(2)/(12)`

Now ,the probability that both are short straws =
`(2)/(12) * (3)/(13)`

=
`(6)/(156)`

=
`(1)/(26)`

Thus Option A is correct.

Hence ,the probability that both are short straws is
`(1)/(26)` .

Answer 2

The right answer is A option.