Question

Answer this Venn diagram Question. I will make you brainliest +50 points.​

Answer 1

Here is the answer!

Answer 2

Answer:

See Figure 1  for answers to (i), (ii)

(iii) 0.10

(iv) Figure 2 in attached image

Step-by-step explanation:

I have drawn the completed figure and explaining each step below. You will have to draw separate figures for each question if you want to give separate figures

Note X represents the entire blue region and the overlapping yellow region = 90 students (given)

Y represents the shaded region and the overlapping region = 35 (given)

The number outside the circles but inside the Venn diagram represents the students in other grades who do not use the net = 50 (given)

The overlapping yellow region shows the number of students who are in both sets ie the students who are in 11th grade and do not use the internet = 25 (computed)

The blue region represents the set of students who are in 11th grade but do not use the net=65(computed)

(i) The shaded area shows the set of students who use the internet but are studying in other grades

(iii) The number of students studying in other grades who do not use the internet is shown at the bottom = 50

(iii) The completed figure shows the number of students in each category. These were computed as follows

The equation used is

X ∪ Y = X + Y - X∩Y  (1)

X ∪ Y is the set of students who are in grade 11 or use the internet or are both

X∩Y is the set of students who are in grade 11 and use the internet

To find XUY note that the complement of XUY ie (XUY)' are those students who do not use the net and are in other grades. This means the number of students who use the net or are in grade 11 or both = 150-50 = 100

Plugging these values into (1) we get
100 = X + Y - X∩Y = 90 + 35 - X∩Y = 125 - X∩Y

100-125 = -(X∩Y)

X∩Y = 25 (Answer iii)

(iv) X' is the complement of X ie the number of students who are not in grade 11. This is 150-90 = 60

X'∩Y is the number of students who are not in grade 11 and use the internet and that is the shaded region shown (answered in ii). This can be computed by Y - X∩Y = 35-25 = 10

So P(selecting a student who belongs to X'∩Y) = 1/10 = 0.1

(v) If all students who use the internet are grade 11 students then the Y circle will be completely inside the X circle
(see Fig 2)

Note: While Venn diagrams are great to visualize the relationships, sometimes they can be confusing during computation of individual values inside them. I personally would check my work(in this case it was a simple exercise) by drawing a table and filling values and computing the missing values. The table below shows the numbers. X and Y have the semantics of the original problem and the cells correspond to the intersection of two of the sets. Thus the top left cell is the number relating to X∩Y, the bottom left cell the number representing  X'∩Y' etc (see figure 3)

In this table, I have indicated the given values in red and the computed values in black. We are able to compute every unknown value by using just the 4 given values. These are called contingency tables and you can search for them if interested.