Trivial question about interpreting probability Please excuse the trivial nature of this question but I can't convince myself of the correct answer.
Suppose there are two events $A$ and $B$ with probabilities:
$p(A)=\frac{1}{3}$ and $p(B)=\frac{2}{9}$
The question is, "How much more likely is event $A$ than $B$?"
My initial answer was $A$ was $1.5$ times more likely than $B$.
Whilst discussing the problem with the problem with a friend they suggested the $A$ was $\frac{1}{9}$ more likely than $B$.  
We both agreed that saying $1.5$ times more likely made sense mathematically and is a natural phrase to use in English.  The discussion arose as to whether the $\frac{1}{9}$ more sentence was just unusual grammar or hides some error mathematically?
My feeling is that it is incorrect somehow but can't quite say why.
Any comments would be gratefully received.
 A: It's just two ways of saying the same thing and both are correct. why? here's why:


*

*you explicitly used the word "times": "...My initial answer was A was 1.5 times more likely than B..."

*when expressing difference "times" was not used: "...A was 1/9 [no use of times] more likely than B..."

A: It is definitively unusual grammar. While the statement is ambiguous because it is not clear whether you are referring to $\frac 19$ of $1$ or $\frac 19$ of $B$, the latter is assumed in common usage.
The ambiguity is more clear with percentages: If your wallet contains 20% of your salary, and you win 10% more on a scratch ticket, do you now have 30% or 22% of your salary?
A: Compared to what? All the events or only the cases when A and B occur?
The probability of A is 1/9 higher to occur when you compare the events of A to B when you look at the total number of events. If you compare only the events that include A or B, than the answer is 1.5.
A: I guess I would never say that $A$ was $1/9$ was more likely than $B$, because I think the general interpretation of that would be $P(A) = (10/9) P(B)$.  I might say something like the probability of $A$ is $1/9$ greater than the probability of $B$, or (even better) the probability of $A$ is greater than the probability of $B$ by $1/9$ (cf. "greater than $\ldots$ by a factor of $10/9$").
I would also not say $A$ was $1.5$ times more likely than $B$; I would say that $A$ is $1.5$ times as likely as $B$.  "More likely" leaves it unclear whether $A$ is $1.5$ times or $2.5$ times as likely as $B$—the same problem that results from expressions such as "Pat's fund is $150$ percent larger than Mark's fund."
