Probability help

I've been sat here for an hour now trying to make sense of these questions, but I really don't have a clue. A bit of help would be much appreciated right now

Reply 1

ghostwalker

Original post by TwiMaster

I've been sat here for an hour now trying to make sense of these questions, but I really don't have a clue. A bit of help would be much appreciated right now

What's causing the problem? Is it the notation for the set/event definitions?

Reply 2

TwiMaster

Original post by ghostwalker

What's causing the problem? Is it the notation for the set/event definitions?

No, I'm okay with understanding the sets in this case. I just can't get my head around the questions

(edited 8 years ago)

Reply 3

TwiMaster

Guys, how would I answer parts a.) and b.) ?

Reply 4

Notnek

Original post by TwiMaster

I've been sat here for an hour now trying to make sense of these questions, but I really don't have a clue. A bit of help would be much appreciated right now

Writing the sets in a simpler way may help:

A = {female residents}
B = {non-smoking residents}
C = {non-over weight residents}

Now what does A ∩ B ∩ C mean?

Reply 5

TwiMaster

Original post by notnek

Writing the sets in a simpler way may help:

A = {female residents}
B = {non-smoking residents}
C = {non-over weight residents}

Now what does A ∩ B ∩ C mean?

Female residents who are non-smoking and are not overweight

Reply 6

Notnek

Original post by TwiMaster

Female residents who are non-smoking and are not overweight

Correct. So how can that set be equal to the set of female residents?

Reply 7

TwiMaster

Original post by notnek

Correct. So how can that set be equal to the set of female residents?

I still don't get how they could be equal to one-another

Reply 8

Notnek

Original post by TwiMaster

I still don't get how they could be equal to one-another

Here's an example:

A = {a, b, c}
B = {a, b, c, d}
C = {a, b, c, d, e}

A ∩ B ∩ C = {a, b, c} = A

Let me know if you don't understand this example.

Think about what had to happen in this question for A ∩ B ∩ C to be equal to A. Then try to apply this idea to your question.

Reply 9

TwiMaster

Original post by notnek

From what I can see from your example, A is a subset of both B and C thus meaning that all the elements in A are also contained in B and C so A ∩ B ∩ C = A

Reply 10

Notnek

Original post by TwiMaster

From what I can see from your example, A is a subset of both B and C thus meaning that all the elements in A are also contained in B and C so A ∩ B ∩ C = A

That's correct and this as it is may be OK as an answer.

But thinking about your specific question : what does this tell you about all the female residents?

Reply 11

TwiMaster

Original post by notnek

That's correct and this as it is may be OK as an answer.

But thinking about your specific question : what does this tell you about all the female residents?

All the females are neither smokers or overweight?

Reply 12

Notnek

Original post by TwiMaster

All the females are neither smokers or overweight?

Correct

Have another go at the next question and post your ideas if you are still stuck.

Reply 13

TwiMaster

Original post by notnek

Correct

Have another go at the next question and post your ideas if you are still stuck.

Thank you! I definitely wouldn't have gotten that one

I think part b.) is implying that those who are overweight do not smoke

Reply 14

Notnek

Original post by TwiMaster

Thank you! I definitely wouldn't have gotten that one

I think part b.) is implying that those who are overweight do not smoke

Correct again.

Is c) OK?

Reply 15

TwiMaster

Original post by notnek

Correct again.

Is c) OK?

Yay, Is c.) saying that being male is independent of being a smoker?

Reply 16

TwiMaster

Does anybody know how to answer part c.) ?

Reply 17

ghostwalker

Original post by TwiMaster

Yay, Is c.) saying that being male is independent of being a smoker?

I presume you mean part d).

'Fraid not. And you want to be careful using the terms "independent" and similar, as they have a specific meaning in probability and statistics.

You've identified that one set represents male residents, and one represents non-smokers. What's the equality sign telling you?