Question

The results of surveying 100 residents of a city reported that 40 read the daily morning paper, 70 read the daily evening paper & 20 read neither. How many:
1. Read at least 1 paper?
2. Read both?
3. Read exactly one daily paper?

Answer 1

1. 100 - 20 = 80

2. 100 - (100 - 70) - (100 - 40) = 10

3. 80 - 10 = 70

Answer 2

thanks but for my answer key its 2) 30 c)50

Answer 3

If you have to post another question, that means you didn't master it yet.

Answer 4

i didn't master these problems?

Answer 5

ya i have the answer for it...i would just like to check it and discuss it

Answer 6

Maybe @apoorvk thought you did

Answer 7

no this is another question

Answer 8

They're similar questions, however

Answer 9

You have three independent events and you have to find probabilities based on these events.

Answer 10

ya its all probability and venn diagrams...i know more or less how to get it but my problem is using the correct formula to get it

Answer 11

for instance this is how i would get it (but not sure if theres a better formula)

Answer 12

Well, using a different setup might help.

Answer 13

well thats why i am here to ask for suggestions

Answer 14

for instance it says 100 respondents were surveyed and 20 ppl said they read none so 100-20= 80 so 80 have to read at least ONE

Answer 15

for both: well i see that 40 ppl raed morning and 70 ppl read evening so thats a total of 110 distributed newspaper so 110 newspaper-80 (who read at least one) = 30?

Answer 16

so theres an extra 30 newspaper left, which means 30 must read an extra one

Answer 17

so for reading exactly one 70-30= 40 evening
40-10= 10 morning

like in my head i can see how it plays out...but i struggle trying to find the correct formu

Answer 18

Well well.. let us call Mr. Venn, and draw a Venn Diagram here

Hmm so let S be the sample space of the 100 people being surveyed. Region A= represents no. of morning readers, and region B = the no. of evening readers
So,

nS=100
nA=40
nB=70

Now ofcourse the total no. of people who read any or atleast one newspaper is 100-20, since 20 don't read any. so, no. of readers (atleast one) =80
And, if you notice no. of readers is the union of setA and setB, since it includes morning and evening readers both.
so, n(AUB) = 80

And (AintersectionB) is the set of people who read BOTH newspapers.



now, if you have studied set theory,

n(AUB) = nA + nB - n(AintersectionB)

so, n(AintersectionB) = 70 + 40 - 80 = 30
(In case you don't understand that, try to think analytically, or else I 'll explain it to you)


And so, if 30 people read both newspapers, the rest of the readers, i.e. 80-30 = 50 read just one of the two newspapers.