# Thread: Mathematical symbols representing probability events

1. ## Mathematical symbols representing probability events

A number of multiple choice questions which I am working on relate to mathematical symbols which represent probability events…in order to tackle the questions, I need to be clear what is/ is not a valid mathematical symbol…. Are a, b, c, d (see below) valid mathematical symbols which can be used to represent a probability event? I think a, b and c are valid symbols, but am not sure about d - can a single letter be used to represent a probability event? I would appreciate any clarification on these symbols i.e. confirmation they are/ are not valid probability symbols. Thanks in advance.

a) S ∩ R (intersection)
b) S R (union)
c) ~S (complement)
d) S

NB
S stands for swimming, R stands for running

2. they look good..the complement of a set can also be written as $S^c$ or $S'$

3. ## Single letter as mathematical symbol in probability

Thanks very much. I just want to be sure that a single letter is valid as a mathematical symbol in probability – this is not made clear in the textbook I am using and I have not been able to locate any internet resources which clarify this. Could you advise as to whether the following list of definitions is correct? I know the first 3 are correct, I just need clarification on the validity of the single letters – I am probably overthinking this but just wanted to doublecheck!

S ∩ D (intersection) represents the probability of swimming and running
S D (union) represents the probability of swimming or running
~S (complement) represents the probability of not swimming
S simply represents the probability of swimming
R simply represents the probability of running

4. I would prefer to represent an event with a letter.

and the probability of the event occuring as $Pr(S)$

Could you post your original question? Things might be a little clear after that.

5. ## Original question

Originally Posted by harish21
I would prefer to represent and event with a letter.

and the probability of the event occuring as $Pr(S)$

Could you post your original question? Things might be a little clear after that.
Thanks, Harish. The questions below all deal with the following scenario. I would simply like confirmation that “S” is a valid mathematical symbol so that I can answer the questions properly. (I am not asking for answers to the questions). I hope the information below helps.

SCENARIO:

Smoking and excessive drinking (of alcoholic beverages) are considered risk factors for heart disease. A team of researchers wishes to see if those who give up drinking or smoking after a first heart attack fare any better than those who do not. They identify patients who arrived at local hospitals with a first heart attack and were found to be smokers or serious drinkers. From these they obtain a group of volunteers for follow-up study. The researchers will monitor a host of variables measuring coronary health as the study progresses but for the questions below we are only interested in the smoking and drinking patterns or the participants. We will let D be the event the patient still drinks and S the event the patient still smokes. The study begins with 80 patient participants. Of these, 60 have quit smoking, 44 have quit drinking, and 32 have abandoned both habits.

QUESTION: We know that 60 have quit smoking. What is the mathematical symbol for this event?
Hint: Review the definitions of D and S above.
S ∩ D (intersection)
S D (union)
~S (complement)
S
none of the above

QUESTION: Give the mathematical symbol for the event whose probability you found in the question immediately above.

S ∩ D (intersection)
S D (union)
~S (complement)
S
none of the above

QUESTION: Give the mathematical symbol for the event whose probability you found in the question immediately above.
S ∩ D (intersection)
S D (union)
~S (complement)
S
none of the above

6. Yes, it is perfectly fine to denote the event that a person smokes with the letter S.