Name: Manny

Who is asking: Student

Level: Secondary

Question:

In a certain school, it is known that 80% of the students use the internet for school projects, 60% use e-mail on a regular basis, and 90% use the internet for school projects or for e-mail on a regular basis. a student from this school is selected at random

Determine thge probability that the student used e-mail, given that the student used the internet for school projects.

ANS: how can i solve this question by useing the vin diaagram

Hi Manny,
For Venn diagram you will draw two circles with intersection. The first
circle, for example I, will be for students who use Internet, the
second, for example E, will be for students who use e-mail. Then you
have:

P(I)=.80, P(E)=.60 and P(I or E)=.90.
From here,
P(I or E)= P(I) +P(E) - P(I and E),
This allows you to find P(I and E), which is the area in the intersection of two circles.
Now you can find P(E given that I), the probability that the student used e-mail, given that the student used the internet for school projects, using the definition that,
P(E given that I) = P(I and E)/ P(I)
Andrei