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, determine how many students have memberships to all 3 OTT: Hotstar, Netflix and Amazon Prime?
Answers
Answer:
Let M, P and C denote the students studying Mathematics, Physics and Chemistry
And U represents total students
So, n(U)=200,
n(M)=120,n(P)=90
n(C)=70,n(M∩P)=40,n(P∩C)=30
n(M∩C)=50,n(M∪P∪C)
′
=20
∴n(M∪P∪C)
′
=n(U)−n(M∪P∪C)
⇒20=200−n(M∪P∪C)
⇒n(M∪P∪C)=180
⇒n(M∪P∪C)=n(M)+n(P)+n(C)
−n(M∩P)−n(P∩C)−n(C∩M)+n(C∩M∩P)
∴180=120+90+70−40−30−50+n(C∩M∩P)
⇒180=280−120+n(C∩M∩P)
⇒n(P∩C∩M)=300−280=20
Hence, the number of students studying all three subjects is 20.
Given : a survey among 230 students in Nilgiri house of IITM BSc degree
all students have at least one OTT subscription
To Find: how many students have memberships to all 3 OTT: Hotstar, Netflix and Amazon Prime
Solution:
n(Total) = 230
n(H) = 90
n(N) = 110
n(A) = 120
n(H ∩ N) = 30
n (H ∩ A) = 30
n (N ∩ A) = 40
n(H ∩ N ∩ A ) = ?
n(none) = 0
n(Total) = n(H) + n(N) + n(A) - n(H ∩ N) - n (H ∩ A) - n (N ∩ A) + n(H ∩ N ∩ A ) + n(none)
=> 230 = 90 + 110 + 120 - 30 - 30 - 40 + n(H ∩ N ∩ A ) + 0
=> 230 = 220 + n(H ∩ N ∩ A )
=> n(H ∩ N ∩ A )= 10
Hence 10 students have memberships to all 3 OTT: Hotstar, Netflix and Amazon Prime
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