Question

Americans like at least one of cheese or apples. A survey shows that $63$% of the Americans like cheese while $76$% like apples. If $x$ % of the Americans like both cheese and apples, then

• A. $x=39$
• B. $x=63$
• C. $3\le x\le 63$
• D. None of these

Answer 1

The correct option is A $x=39$

Given $A$ be the percent of americans like cheese

$B$ be the percent of americans like apples

$p\left(A\right)=\frac{63}{100}=0.63$

$p\left(B\right)=\frac{76}{100}=0.76$

Let $p(A\cap B)=x$

$p(A\cup B)=1$ as every american likes either cheese or apples

$p(A\cup B)=p\left(A\right)+p\left(B\right)-p(A\cap B)$

$1=0.63+0.76-x$

$x=1.39-1$

$x=0.39\Rightarrow x=0.39\times 100=39\%$