Question

in a class of 150 students, 45 take history, 65 take geography and 10 take both history and geography. how many students did not take any of these two subject

1)30
2)10
3)50
4) 40​

Answer 1

Answer:

therefore the answer will be option no.2 10

Step-by-step explanation:

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Answer 2

Given:

Total no. of students = N = 150

No. of students who take history = n(H) = 45

No. of students who take geography= n(G) = 65

No. of students who take both history and geography = n(H ∩ G) = 10

To Find:

No of the students did not take any of these two subjects

Solution:

No. of students who take history or geography =

n(H ∪ G) = n(H) + n(G) - n(H ∩ G)

n(H ∪ G) = 45 + 65 - 10

n(H ∪ G) = 100

so, No. of students take history or geography = 100

⇒ No of the students did not take any of these two subjects =

Total no of students -  No. of students take history or geography

⇒ No of the students did not take any of these two subjects =

   N - n( H∪G )

= 150 -100

= 50

Hence, No of the students who did not take any of these two subjects is 50.