Question

In a survey among 230 students in Nilgiri house of IITM BSc degree, the following data were found: 90 students have Hotstar subscription 110 students have Netflix subscription 120 students have Amazon Prime subscription. 30 students have both Hotstar and Netflix subscription whereas 30 students have both Hotstar and Amazon Prime and 40 students subscribe to both Netflix and Amazon Prime. Assuming that all students have at least one OTT subscription, detemine how many students have memberships to all 3 OTT: Hotstar, Netflix and Amazon Prime? ​

Answer 1

Answer:

10

Step-by-step explanation:

Answer 2

Given:

No. of students in survey = 230

No. of students having Hotstar subscription = 90

No. of students having Netflix subscription = 110

No. of students having Amazon Prime subscription = 120

No. of students having both Hotstar and Netflix = 30

No. of students having both Hotstar and Amazon Prime = 30

No. of students having both Netflix and Amazon Prime = 40

To find:

No. of students have subscriptions to all 3 OTT.

Solution:

Let Hotstar subscription be H, Netflix subscription be N and Amazon Prime subscription be A.

n(H∪A∪N)=230,n(H)=90,n(N)=110,n(A)=120

n(H∩N) = 30, n(H∩A) = 30, n(N∩A) = 40, n(H∩A∩N) = ?

n(H∪A∪N) = n(H) + n(A) + n(N) - n(H∩N) - n(H∩A) - n(N∩A) + n(H∩A∩N)

n(H∩A∩N) = n(H∪A∪N) - n(H) - n(A) - n(N) + n(H∩N) + n(H∩A) + n(N∩A)

n(H∩A∩N) $=230-90-110-120+30+30+40$

n(H∩A∩N) $=10$

No. of students having subscription to all 3 OTTs are 10.