Question

In a group of people:

• 70 play only Hockey.

• 100 play only Football.

• 30 play both Hockey and Football.

• 150 play neither game.
What percentage of the people play Hockey?

• A. \(28.57\%\)
• B. \(46.6\%\)
• C. \(66.6\%\)
• D. \(20\%\)

Hint:

While finding the number of people in a set, always include those who belong exclusively to the set as well as those belonging to the intersection.

Answer 1

The Correct Option is A

Step 1: Read the four groups.
We are told $70$ people play only Hockey, $100$ play only Football, $30$ play both games, and $150$ play neither. Let us treat each group as a separate non-overlapping piece.
Step 2: Build the total head count.
Since the four pieces have no overlap left in them, the whole group is just their sum: \[ 70+100+30+150=350 \]
Step 3: Decide who counts as a Hockey player.
A Hockey player is anyone whose set includes Hockey, that is the only-Hockey people plus the both-games people.
Step 4: Add those two pieces.
\[ 70+30=100 \] So $100$ people play Hockey in total.
Step 5: Turn the count into a percentage.
\[ \frac{100}{350}\times 100 \]
Step 6: Simplify the fraction.
\[ \frac{100}{350}=\frac{2}{7}=0.2857\ldots \] so the percentage is about $28.57\%$.
\[ \boxed{28.57\%} \]