# in a class of 70 students, 6 offer economics only, 18 offer economics but mathematics, 36 offer economics and geography, 53 offer economics, 50 offer geography and 34 offer mathematics and geography. All students offer atleast one subject.

a. illustrate this information in a Venn diagram

b. determine the number of students who offer

i. mathematics

ii. mathematics and geography but not economics

iii. the probability that a student selected at random from the class offers geography only

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1. Cannot draw Venn diagram on these posts.

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2. Draw 3 overlapping circles and label them E, M, and G for the subjects
We have no information about how many take all 3,

1. so place x in the intersection of all 3, (the innermost part)
2. place 6 in the part of E not intersecting anything else
3. I assume you mean "18 offer economics but NOT mathematics"
so place 12 in the remaining part of the intersection of E and G

4. label the remaining part of the intersection of E and M as "a" and
the remaining part of the intersection of M and G as "b"

5. It said 53 take E, so
a + x + 6 + 12 = 53
a+x = 35

6. We are told that 36 take economics and geography, so
12+x = 36
x = 24
now in a+x = 35 from above
a = 11

Replace the values of x and a in your Venn diagram

7. We are told that 34 take mathematics and geography, so
24 + b = 34
b = 10
replace the b with 10

8. Finally, the total = 70
label the "only M" with d, and the "only G" with c
so we have c + d + 53 + 10 = 70
c + d = 7

9. But it said that 50 take G, so
c + 12+24+10 = 50
c = 4 , which leaves d = 3

Every region has been uniquely labeled, and thus all questions can

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3. MY RESPONSE IS 12 =)

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4. I want an answer of question 1

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5. Understandable

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6. Yes

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7. I dont understand some part

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8. To find the probability is not given

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9. Please show me the diagram

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