One person from a party is selected at random

Question

Here is the question:

John invites 12 friends to a dinner party, half of whom are men. Exactly one man and one woman are bringing desserts. If one person from this group is selected at random, what is the probability that it is a woman, or a man who is not bringing a dessert?

I'm not a native speaker, how should I understand "a woman, or a man who is not bringing a dessert" please?

Should it be construed

(1) a man who is not bringing a dessert or a woman

or

(2) a woman who is not bringing a dessert or a man who is not bringing a dessert

?

Because apparently the answer is different from each other and if I'm not wrong, (1) is 11/12 and (2) is 10/12.

By the way, how would this sentence "a woman who is not bringing a dessert or a man who is not bringing a dessert" be written if it is not "a woman, or a man who is not bringing a dessert"?

I appreciate your help!

Answer 1

I think the question is about to calculate the probability of the person selected is either a woman, or a man without bringing dessert.

Interprete it to logic language, it should be: $$P(woman\bigcup man without dessert)=P(woman)+P(man without dessert)$$

So what you need to do is simple arithmetic, $1/2 + 5/12=11/12$

Btw, since there is a comma at the end of woman, it means that we should consider this sentence separately. Your assumption(2) is making sense if and only if the comma doesn't exist.

Answer 2

As pointed out by JMoravitz, you have correctly identified the answers for both, so well done, and usually you would ask for clarification in a test or something like that.

In my opinion, I would interpret "a woman, or a man who is not bringing a dessert" as (2) a woman who is not bringing a dessert or a man who is not bringing a dessert.

But again, don't stress as this type of ambiguity in a test is rare. The comma is ambiguous, and I might be wrong. In an actual exam, ask for clarification.