A group of 60 students were asked whether they watch TV Patrol or 24 Oras
or both programs (depending on the news). Thirty - eight of these
students watch TV Patrol and 32 watch 24 Oras.
a. How many watch TV Patrol only?
b. How many watch 24 Oras only?
c. How many watch both news programs?
Answers
Answer:
You must know about Venn diagram from which it can easily be solved
Step-by-step explanation:
First we found the common people who watch both by the above formula and the answer of iii) is clear 10
now for i and ii you watch the diagram as 32 people watch 24orals and 10 people watches both now we must remove the people who watches both programs to get our required ans. similarily in case of TV patrol
ans will be i) 22
ii)28
Given : A group of 60 students were asked whether they watch TV Patrol or 24 Oras or both programs
38 students watch TV Patrol
32 watch 24 Oras.
To Find : a. How many watch TV Patrol only?
b. How many watch 24 Oras only?
c. How many watch both news programs?
Solution:
Total = 60
n(A) = watch TV Patrol = 38
n(B) = watch 24 Oras. = 32
n ( A ∩ B) = watch Both
none = watch none = x
Total = n(A) + n(B) - n ( A ∩ B) + x
=> 60 = 38 + 32 - n ( A ∩ B) + x
=> n ( A ∩ B) = 10 + x
watch TV Patrol only = n(A) - n ( A ∩ B)
= 38 - (10 + x)
= 28 - x
watch 24 Oras only = n(B) - n ( A ∩ B)
= 32 - (10 + x)
= 22 - x
watch both news programs
n ( A ∩ B) = n(A) + n(B) - n ( A ∩ B)
= 38 + 32 - (10 + x)
= 60 - x
If x = 0
Then watch TV Patrol only = 28
watch 24 Oras only = 22
watch both news programs = 60
if x = 22 ( max possible values)
Then watch TV Patrol only = 6
watch 24 Oras only = 0
watch both news programs = 38
Hence watch TV Patrol only is between 6 and 28
watch 24 Oras only is between 0 and 22
watch both news programs is between 38 and 60
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