Answer:
15 Respondents
Step-by-step explanation:
Total number of respondents = n (PUBG ∪ M ∪ C) = 50
PUBG = n(PUBG ) = 15 people
Mobile legends = n(M) = 30 people
Clash of clans = n(C) = 20 people
n ( PUBG ∩ M) = Unknown
Step 1
The first step is to find the number of respondents that chose two or the games
a) Number of respondents that chose Mobile legends and PUBG =
n ( M ∩ PUBG)
30 - x = 15 - x + x
30 - 15 = x + x - x
15 = x
b) a) Number of respondents that chose Mobile legends and Clash of clans =
n ( M ∩ C)
n ( M ∩ C) = y
30 - y = 20 - y + y
30 - 20 = y + y - y
10 = y
c) Number of respondents that chose PUBG and Clash of clans =
n ( C ∩ PUBG) = z
20 - z = 15 - z + z
20 - 15 = z + z - z
5 = z
Step 2
How many Respondents chose all 3 online games
= n ( PUBG ∩ M)
n (PUBG ∪ M ∪ C) = n(PUB ) + n ( M ) + n (C) – n ( M ∩ PUBG) – n ( C ∩ PUBG) – n ( M ∩ C) + n (PUBG ∩ M ∩ C)
50 = 30 + 20 + 15 - 15 - 5 - 10 + n (PUBG ∩ M ∩ C)
50 = 65 - 30 + n (PUBG ∩ M ∩ C)
50 = 35 + n (PUBG ∩ M ∩ C)
50 - 35 = n (PUBG ∩ M ∩ C)
n (PUBG ∩ M ∩ C) = 15
Therefore, the number of Respondents chose all 3 online games = 15
