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.

Question

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.

Answer 1

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