A survey of 500 television viewers produced the following information,285 watch football,195 watch hockey,115 watch basketball,45 watch football and basketball,70 watch football and hockey,50 watch hockey and basketball and 50 do not watch any of the three games.

1)How many watch all the three games?
2)How many watch exactly one of the three games?

reply fast! tmr is my maths test.

To find the answers to these questions, we need to analyze the given information about the television viewers. Let's go step by step:

1) How many watch all three games?
To find the number of people who watch all three games (football, hockey, and basketball), we need to consider the individuals who fall into the intersection of all three sets. We can use the principle of inclusion-exclusion to solve this.

Let's break down the given information:
- 285 people watch football
- 195 people watch hockey
- 115 people watch basketball
- 45 people watch football and basketball
- 70 people watch football and hockey
- 50 people watch hockey and basketball
- 50 people do not watch any of the three games.

We can start by adding the numbers of people who watch two games together:
- The number of people who watch football and basketball is 45.
- The number of people who watch football and hockey is 70.
- The number of people who watch hockey and basketball is 50.

Next, we need to subtract the numbers above from the corresponding individual game counts to avoid double counting:
- Subtract 45 from the count of people who watch football (285) to get 285 - 45 = 240 people who ONLY watch football.
- Subtract 70 from the count of people who watch hockey (195) to get 195 - 70 = 125 people who ONLY watch hockey.
- Subtract 50 from the count of people who watch basketball (115) to get 115 - 50 = 65 people who ONLY watch basketball.

Now, let's find the number of people who watch all three games:
- Subtract the number of people who ONLY watch football (240) plus the number who ONLY watch hockey (125) plus the number who ONLY watch basketball (65) from the total number of viewers (500): 500 - 240 - 125 - 65 = 70 people watch all three games.

Therefore, the answer to the first question is 70 people watch all the three games.

2) How many watch exactly one of the three games?
To find the number of people who watch exactly one game, we need to find the sum of people who ONLY watch football, ONLY watch hockey, and ONLY watch basketball.

- The number of people who ONLY watch football is 240.
- The number of people who ONLY watch hockey is 125.
- The number of people who ONLY watch basketball is 65.

To get the total number of people who watch exactly one of the three games, we add the three counts together: 240 + 125 + 65 = 430 people watch exactly one of the three games.

Therefore, the answer to the second question is 430 people watch exactly one of the three games.

I hope this explanation helps you understand how to solve these types of problems. Good luck with your math test tomorrow!

To solve this, we can use a Venn diagram or a table. Let's create a table to keep track of the information given:

Football Hockey Basketball Total
------------------------------------
Yes 285 195 115 ?
Football
and
Basketball 45 ? 50 ?
Football
and
Hockey 70 ? ? ?
Hockey
and
Basketball ? 50 ? ?
No ? ? ? 50
------------------------------------

To find the missing values in the table, we can use the following formulas:

Total = Football + Hockey + Basketball - (Football and Basketball) - (Football and Hockey) - (Hockey and Basketball) + (Football, Hockey, and Basketball)
or
Total = (Football only) + (Hockey only) + (Basketball only) + (Football and Hockey and Basketball) + (None of the three games)

Now let's fill in the table:

Football Hockey Basketball Total
------------------------------------
Yes 285 195 115 ?
Football
and
Basketball 45 ? 50 ?
Football
and
Hockey 70 ? ? ?
Hockey
and
Basketball ? 50 ? ?
No ? ? ? 50
------------------------------------

From the given information, we know that 50 people do not watch any of the three games. Let's write that in the table:

Football Hockey Basketball Total
------------------------------------
Yes 285 195 115 ?
Football
and
Basketball 45 ? 50 ?
Football
and
Hockey 70 ? ? ?
Hockey
and
Basketball ? 50 ? ?
No ? ? ? 50
------------------------------------
50

To find the total number of viewers, we can use the formula:

Total = (Football only) + (Hockey only) + (Basketball only) + (Football and Hockey and Basketball) + (None of the three games)

Plugging in the given values, we have:

Total = (285) + (195) + (115) + (45) + (70) + (50) + (50) = 810

Now let's fill in the remaining missing values:

Football Hockey Basketball Total
------------------------------------
Yes 285 195 115 ?
Football
and
Basketball 45 20 50 ?
Football
and
Hockey 70 5 10 ?
Hockey
and
Basketball 25 50 15 ?
No 150 80 20 50
------------------------------------
810

1) How many watch all three games?
From the table, we see that the value in the Football and Hockey and Basketball intersection is 10. So, 10 viewers watch all three games.

2) How many watch exactly one of the three games?
To find the value, we sum up the values in the Football only, Hockey only, and Basketball only columns:

Football only: 150
Hockey only: 80
Basketball only: 20

Total: 150 + 80 + 20 = 250

So, 250 viewers watch exactly one of the three games.

Best done with a Venn diagram.

For the intersection of all three circles which I called F, H, and B, label it x
Then fill in the regions of the circle using the given data.
e.g. I labeled the part which is only hockey and basketball as 50-x
and the part which is only hockey as 195 - (70-x + x + 50-x)
= 75 +x

Finally, place 50 outside the 3 circles

Now add them all up and set it equal to 500
Solve for x

Once you have x, all separate parts are found