Probability of three events occurring

[fiksx]

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:

$55\%$ using Twitter ,

$53\%$ using Facebook ,

$20\%$ using Twitter and facebook both,

$19\%$ use both Facebook and
Instagram.

$76\%$ use at least Twitter
and / or Instagram

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

$49\%$ use only one of twitter ,facebook, or instagram
At this time, find the next
ratio respectively.

$1$. Percentage of using both
Twitter and Instagram

$2$. Percentage of using all
of Twitter, Facebook and Instagram

$3$. Percentage of not using
either Twitter, Facebook or Instagram
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 don't 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
$P(T \cup F \cup I) = P(T)+P(F)+P(I)-P(T \cap F) - P(T \cap I) - Ｐ(I \cap F) + P(T \cap F \cap I) =$
$49=55+53+38-20-19-17 +P(T \cap F \cap I)$
$P(T \cap F \cap I)=-41$

 

[member 587159]

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.