# In a survey of 500 T.V. viewers, 285 watched KBC, 195 watch cricket, 115 watch hockey, 45 watch KBC and hockey

#### DAVV MBA PYQ

In a survey of 500 T.V. viewers, 285 watched KBC, 195 watch cricket, 115 watch hockey, 45 watch KBC and hockey, 70 watch KBC and cricket, 50 watch cricket and hockey, 50 do not watch any of three games. How many watch all 3 and how many watch exactly one of three ?
Solution:
K for KBC
H for Hockey
C for Cricket
Formula:
n(K U H U C) = n(K)+n(H)+n(C)-n(K ∩ H)-n(K ∩ C)-n(H ∩ C)+n(K ∩ H ∩ C)
Given,
n(K U H U C) = 500 – 50 = 450
n(K) = 285
n(H) = 115
n(C) = 195
n(K ∩ H) = 45
n(K ∩ C) = 70
n(H ∩ C) = 50
n(K ∩ H ∩ C) = ?
How many watch all the three games ?
n(K U H U C) = n(K)+n(H)+n(C)-n(K ∩ H)-n(K ∩ C)-n(H ∩ C)+n(K ∩ H ∩ C)
450 = 285+115+195-45-70-50+n(K ∩ H ∩ C)
n(K ∩ H ∩ C) = 20
How many watch all 3 ?
Ans. 20
Now, how many watch exactly one ?

From the Venn diagram,
Watch exactly KBC = 190
Watch exactly Hockey = 40
Watch exactly Cricket = 95

#### Practice questions (DAVV MBA PYQs):

Q1. In a city there are 100000 people, 64% of them speak Greek, 55% people speak Latin, 43% people speak French, 21% people speak both Greek and Latin, 31% people speak both Greek and French, and 41% people speak both Latin and French. Determine the number of people speak all the three languages.