# Find the sample space and $\mathbb P(A\cup B)$.

Among 100 people, 20 like meat, 50 like vegetable and 10 like both. Denote $$A$$ the event "the person like meat", $$B$$ the event "the person like vegetable". We take one person at random among the 100 people.

1) Write the sample space and gives the probability measure.

2) What is the probability that the person chosen like meat and vegetable ?

1)a) I have difficulties to write the sample space. Is it

$$\{A\cap B, A\cap B^c, A^c\cap B,A^c\cap B^c\} \ \ ?$$

I think @mfl write the event space instead of sample space in the comment, no ?

b) It's fine.

2) It's fine.

• But it"s not the entire sample space, is it ? Because $A$ is an event, when I write $\mathbb P\{\omega \}$, $\omega \notin\{A,B,A\cup B,A\cap B,\emptyset\}$ @mfl – user601023 Oct 17 '18 at 14:30
• Ok, and is the measure of probability correct ? @mfl – user601023 Oct 17 '18 at 14:47
• So as written (i.e. $\mathbb P\{\omega \}=...$ for $\omega \in A$) doesn't really make sense, right ? I really have to write $\mathbb P(A)=...$\mathbb P(B)=...\$ etc, right ? @mfl – user601023 Oct 17 '18 at 15:24
• @mfl: In fact, don't you confuse sample spaces and event space ? What you wrote looks more as a event space... – user601023 Oct 17 '18 at 18:02
• Yes, you right. I don't know what described @mfl , but it's not the event space. May be he could give more information ? – Surb Oct 17 '18 at 19:36