# Probability of three events occurring

• fiksx
In summary, a questionnaire survey on the use of social media was conducted for students at A University. As a result, we got the following:-##55\%## of students use Twitter-##53\%## of students use Facebook-##20\%## of students use Twitter and Facebook both-##19\%## use both Facebook and Instagram-##76\%## of students use at least Twitter and / or Instagram-##72\%## of students use at least one of Facebook and Instagram-##49\%## of students use only one of Twitter, Facebook, or Instagram.
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:

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 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##

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.

## 1. What is the probability of three independent events occurring?

The probability of three independent events occurring is calculated by multiplying the individual probabilities of each event. For example, if the probability of event A occurring is 0.5, the probability of event B occurring is 0.4, and the probability of event C occurring is 0.3, then the probability of all three events occurring together is 0.5 x 0.4 x 0.3 = 0.06 or 6%.

## 2. How do you calculate the probability of three dependent events occurring?

The probability of three dependent events occurring is calculated by multiplying the conditional probabilities of each event. This means that the probability of each event occurring is affected by the outcome of the previous event. For example, if the probability of event A occurring is 0.5, the probability of event B occurring given that event A has occurred is 0.4, and the probability of event C occurring given that both event A and B have occurred is 0.3, then the probability of all three events occurring together is 0.5 x 0.4 x 0.3 = 0.06 or 6%.

## 3. What is the difference between independent and dependent events?

Independent events are events that have no impact on each other. This means that the outcome of one event does not affect the outcome of the other event. Dependent events, on the other hand, are events that are affected by the outcome of previous events.

## 4. Can the probability of three events occurring be greater than 1?

No, the probability of three events occurring cannot be greater than 1. The highest possible probability is 1, which represents a 100% chance of the events occurring. If the calculated probability is greater than 1, it means that the events are not mutually exclusive and there is an overlap in the possible outcomes.

## 5. How can you use the probability of three events occurring in real-life situations?

The probability of three events occurring can be used in various real-life situations, such as predicting the likelihood of winning a game, the chances of a certain outcome in a scientific experiment, or the probability of a certain event happening in the stock market. It can also be used to make informed decisions, such as determining the best course of action in a business or personal situation.

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