# Probability of three events occurring

## Homework Statement:

probability three event

## Relevant Equations:

i could find ##P(T \cup F) = P(T)+P(F)-P(T \cap F)=55\% +53\%-20\%=88% ## is this right?

##P(T) =35## but i dont know ##P(T \cap I)##
A questionnaire survey on the use of SNS was conducted for students at A University. As a result,
we got the following:

Instagram.

and / or Instagram

##72\%## use at least one of Facebook
and Instagram

At this time, find the next
ratio respectively.

##1##. Percentage of using both

##2##. Percentage of using all

##3##. Percentage of not using

I was confused, for ##P(T\cap F)=20\%## does this also include ##P(T\cap F \cap I )## ?
for ##P(F) ## pnly ##P(F\cap T)##, is it correct only facebook is ##14\%##?
##P(F)=53\% - P(F\cap T) - P(F\cap I)=53\%-19\%-20\% =14\%##?

i could find ##P(T \cup F) = P(T)+P(F)-P(T \cap F)=55\% +53\%-20\%=88% ##
is this right?
##P(T) =35##
but i dont know
##P(T \cap I)##

P(F)=14

i manage to find :
##P(T \cap I) = 17## and ##P(I)=38##
but when i count
##P(T \cup F \cup I) = P(T)+P(F)+P(I)-P(T \cap F) - P(T \cap I) - Ｐ(I \cap F) + P(T \cap F \cap I) = ##
##49=55+53+38-20-19-17 +P(T \cap F \cap I) ##
##P(T \cap F \cap I)=-41##

Related Calculus and Beyond Homework Help News on Phys.org
Math_QED
Homework Helper
2019 Award
Several important remarks to be made here:

(1) A probability is a number in ##[0,1]##. E.g., either write ##P(A) = 0.1## or ##P(A) = 10 \%##, but not ##P(A) = 10##. The latter is just plain wrong.

(2) Because of ##(1)##, negative probabilities aren't allowed. Your answer ##P(T \cap F \cap I) = -41## doesn't make sense because of two reasons!

The trick to solve this exercise is to write what you are looking for in terms of what you have. For example, you have to write the set ##T \cap I## in terms of what has been given. Drawing Venn diagrams might definitely help.