A survey of 550 T.V Watchers produced the following information.285 watch football game,195 watch hockey game,115 watch cricket,45 watch football and cricket, 70 watch football and hockey,50 watch hockey and cricket. 100 do not watch any of three games. (a) How many people watch exactly one of the three games? (b) How many people watch all three games?
Answers
Answer:
Step-by-step explanation:
People watched =total-not watched=550-100=450
a) exactly football=285-(45+70) =170
exactly hockey=195-(70+50) =75
exactly cricket=115-(45+50) =20
b) people watch all the three be x
170+70+75+45+20+50+x=450
on solving, x=20
People watched all the three=20
Given :
Survey required for 550 T.V watchers
285 watch football game
195 watch hockey game
115 watch cricket
45 watch football and cricket
70 watch football and hockey
50 watch hockey and cricket
100 do not watch any of three games
To find :
a. How many people watch exactly one of the three games?
b, How many people watch all three games?
Solution :
Let us assume that the three games watched be X
So,
50 - X = watch hockey and basketball only
70 - X = watch football and hockey only
45 - X = watch football and basketball only
So,
= 115 - (45 - X) - (50 - X) - X
= 115 - 45 + X - 50 + X - X
= 115 - 95 + X
= 20 + X
This 20 + X watch basketball only
Now
= 195 - (70 - X) - (50 - X) - X
= 195 - 70 + X - 50 + X - X
= 195 - 120 + X
= 75 + X
This 75 + X watch hockey only
And,
= 285 - (45 - X) - (70 - X) - X
= 285 - 45 + X - 70 + X - X
= 285 - 115 + X
= 170 + X
This 170 + X watch football only
And give that 100 do not watch any of the three games.
Now for determining the number of people watch exactly one of three games first we have to find out the how number of peoples watched all the three games which are as follows
X + 50 - X + 70 - X + 45 - X + 20 + X + 75 + X + 170 + X + 100 = 550
530 + X = 550
x = 550 - 530
= 20
Now the exactly one of the three games is
= 20 + X + 75 + X + 170 + X
= 265 + 3X
= 265 + 3 × 20
= 265 + 60
= 325
Hence, the 325 people watch exactly one of the three games
And, the 20 people watch all three games
Learn more
A survey of 500 television watchers
produced the information:
285 watch football games
195 watch hockey games
115 watch basketball games
45 watch football and basketball
70 watch football and hockey
50 watch hockey and basketball
50 do not watch any of the three games
A. how many people in the survey watch all the three games?
B. How many people watch exactly one of the three games?
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